3x+7-2x-3=2

Add 2x-3 to both sides of the equation.

3x+7=2+2x-3

To remove the radical on the left side of the equation, square both sides of the equation.

3x+72=(2+2x-3)2

Multiply the exponents in ((3x+7)12)2.

Apply the power rule and multiply exponents, (am)n=amn.

(3x+7)12⋅2=(2+2x-3)2

Cancel the common factor of 2.

Cancel the common factor.

(3x+7)12⋅2=(2+2x-3)2

Rewrite the expression.

(3x+7)1=(2+2x-3)2

(3x+7)1=(2+2x-3)2

(3x+7)1=(2+2x-3)2

Simplify.

3x+7=(2+2x-3)2

3x+7=(2+2x-3)2

Simplify (2+2x-3)2.

Rewrite (2+2x-3)2 as (2+2x-3)(2+2x-3).

3x+7=(2+2x-3)(2+2x-3)

Expand (2+2x-3)(2+2x-3) using the FOIL Method.

Apply the distributive property.

3x+7=2(2+2x-3)+2x-3(2+2x-3)

Apply the distributive property.

3x+7=2⋅2+22x-3+2x-3(2+2x-3)

Apply the distributive property.

3x+7=2⋅2+22x-3+2x-3⋅2+2x-32x-3

3x+7=2⋅2+22x-3+2x-3⋅2+2x-32x-3

Simplify and combine like terms.

Simplify each term.

Multiply 2 by 2.

3x+7=4+22x-3+2x-3⋅2+2x-32x-3

Move 2 to the left of 2x-3.

3x+7=4+22x-3+2⋅2x-3+2x-32x-3

Multiply 2x-32x-3.

Raise 2x-3 to the power of 1.

3x+7=4+22x-3+22x-3+2x-312x-3

Raise 2x-3 to the power of 1.

3x+7=4+22x-3+22x-3+2x-312x-31

Use the power rule aman=am+n to combine exponents.

3x+7=4+22x-3+22x-3+2x-31+1

Add 1 and 1.

3x+7=4+22x-3+22x-3+2x-32

3x+7=4+22x-3+22x-3+2x-32

Rewrite 2x-32 as 2x-3.

Use axn=axn to rewrite 2x-3 as (2x-3)12.

3x+7=4+22x-3+22x-3+((2x-3)12)2

Apply the power rule and multiply exponents, (am)n=amn.

3x+7=4+22x-3+22x-3+(2x-3)12⋅2

Combine 12 and 2.

3x+7=4+22x-3+22x-3+(2x-3)22

Cancel the common factor of 2.

Cancel the common factor.

3x+7=4+22x-3+22x-3+(2x-3)22

Divide 1 by 1.

3x+7=4+22x-3+22x-3+(2x-3)1

3x+7=4+22x-3+22x-3+(2x-3)1

Simplify.

3x+7=4+22x-3+22x-3+2x-3

3x+7=4+22x-3+22x-3+2x-3

3x+7=4+22x-3+22x-3+2x-3

Subtract 3 from 4.

3x+7=1+22x-3+22x-3+2x

Add 22x-3 and 22x-3.

3x+7=1+42x-3+2x

3x+7=1+42x-3+2x

3x+7=1+42x-3+2x

Since the radical is on the right side of the equation, switch the sides so it is on the left side of the equation.

1+42x-3+2x=3x+7

Move all terms not containing 2x-3 to the right side of the equation.

Subtract 1 from both sides of the equation.

42x-3+2x=3x+7-1

Subtract 2x from both sides of the equation.

42x-3=3x+7-1-2x

Subtract 2x from 3x.

42x-3=x+7-1

Subtract 1 from 7.

42x-3=x+6

42x-3=x+6

Divide each term by 4 and simplify.

Divide each term in 42x-3=x+6 by 4.

42x-34=x4+64

Cancel the common factor of 4.

Cancel the common factor.

42x-34=x4+64

Divide 2x-3 by 1.

2x-3=x4+64

2x-3=x4+64

Cancel the common factor of 6 and 4.

Factor 2 out of 6.

2x-3=x4+2(3)4

Cancel the common factors.

Factor 2 out of 4.

2x-3=x4+2⋅32⋅2

Cancel the common factor.

2x-3=x4+2⋅32⋅2

Rewrite the expression.

2x-3=x4+32

2x-3=x4+32

2x-3=x4+32

2x-3=x4+32

To remove the radical on the left side of the equation, square both sides of the equation.

2x-32=(x4+32)2

Simplify each side of the equation.

Multiply the exponents in ((2x-3)12)2.

Apply the power rule and multiply exponents, (am)n=amn.

(2x-3)12⋅2=(x4+32)2

Cancel the common factor of 2.

Cancel the common factor.

(2x-3)12⋅2=(x4+32)2

Rewrite the expression.

(2x-3)1=(x4+32)2

(2x-3)1=(x4+32)2

(2x-3)1=(x4+32)2

Simplify.

2x-3=(x4+32)2

2x-3=(x4+32)2

Solve for x.

Simplify (x4+32)2.

Rewrite (x4+32)2 as (x4+32)(x4+32).

2x-3=(x4+32)(x4+32)

Expand (x4+32)(x4+32) using the FOIL Method.

Apply the distributive property.

2x-3=x4(x4+32)+32(x4+32)

Apply the distributive property.

2x-3=x4⋅x4+x4⋅32+32(x4+32)

Apply the distributive property.

2x-3=x4⋅x4+x4⋅32+32⋅x4+32⋅32

2x-3=x4⋅x4+x4⋅32+32⋅x4+32⋅32

Simplify and combine like terms.

Simplify each term.

Multiply x4⋅x4.

Multiply x4 and x4.

2x-3=x⋅x4⋅4+x4⋅32+32⋅x4+32⋅32

Raise x to the power of 1.

2x-3=x1x4⋅4+x4⋅32+32⋅x4+32⋅32

Raise x to the power of 1.

2x-3=x1x14⋅4+x4⋅32+32⋅x4+32⋅32

Use the power rule aman=am+n to combine exponents.

2x-3=x1+14⋅4+x4⋅32+32⋅x4+32⋅32

Add 1 and 1.

2x-3=x24⋅4+x4⋅32+32⋅x4+32⋅32

Multiply 4 by 4.

2x-3=x216+x4⋅32+32⋅x4+32⋅32

2x-3=x216+x4⋅32+32⋅x4+32⋅32

Multiply x4⋅32.

Multiply x4 and 32.

2x-3=x216+x⋅34⋅2+32⋅x4+32⋅32

Multiply 4 by 2.

2x-3=x216+x⋅38+32⋅x4+32⋅32

2x-3=x216+x⋅38+32⋅x4+32⋅32

Move 3 to the left of x.

2x-3=x216+3⋅x8+32⋅x4+32⋅32

Multiply 32⋅x4.

Multiply 32 and x4.

2x-3=x216+3×8+3×2⋅4+32⋅32

Multiply 2 by 4.

2x-3=x216+3×8+3×8+32⋅32

2x-3=x216+3×8+3×8+32⋅32

Multiply 32⋅32.

Multiply 32 and 32.

2x-3=x216+3×8+3×8+3⋅32⋅2

Multiply 3 by 3.

2x-3=x216+3×8+3×8+92⋅2

Multiply 2 by 2.

2x-3=x216+3×8+3×8+94

2x-3=x216+3×8+3×8+94

2x-3=x216+3×8+3×8+94

Add 3×8 and 3×8.

2x-3=x216+23×8+94

2x-3=x216+23×8+94

Cancel the common factor of 2.

Factor 2 out of 8.

2x-3=x216+23×2(4)+94

Cancel the common factor.

2x-3=x216+23×2⋅4+94

Rewrite the expression.

2x-3=x216+3×4+94

2x-3=x216+3×4+94

2x-3=x216+3×4+94

Since x is on the right side of the equation, switch the sides so it is on the left side of the equation.

x216+3×4+94=2x-3

Move all terms containing x to the left side of the equation.

Subtract 2x from both sides of the equation.

x216+3×4+94-2x=-3

To write -2x as a fraction with a common denominator, multiply by 44.

x216+3×4-2x⋅44+94=-3

Combine -2x and 44.

x216+3×4+-2x⋅44+94=-3

Combine the numerators over the common denominator.

x216+3x-2x⋅44+94=-3

Find the common denominator.

Multiply 3x-2x⋅44 by 44.

x216+3x-2x⋅44⋅44+94=-3

Combine.

x216+(3x-2x⋅4)⋅44⋅4+94=-3

Multiply 94 by 44.

x216+(3x-2x⋅4)⋅44⋅4+94⋅44=-3

Combine.

x216+(3x-2x⋅4)⋅44⋅4+9⋅44⋅4=-3

Multiply 4 by 4.

x216+(3x-2x⋅4)⋅416+9⋅44⋅4=-3

Multiply 4 by 4.

x216+(3x-2x⋅4)⋅416+9⋅416=-3

x216+(3x-2x⋅4)⋅416+9⋅416=-3

Multiply 9 by 4.

x216+(3x-2x⋅4)⋅416+3616=-3

Combine the numerators over the common denominator.

x2+(3x-2x⋅4)⋅4+3616=-3

Simplify the numerator.

Multiply 4 by -2.

x2+(3x-8x)⋅4+3616=-3

Subtract 8x from 3x.

x2-5x⋅4+3616=-3

Multiply 4 by -5.

x2-20x+3616=-3

Factor x2-20x+36 using the AC method.

Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is 36 and whose sum is -20.

-18,-2

Write the factored form using these integers.

(x-18)(x-2)16=-3

(x-18)(x-2)16=-3

(x-18)(x-2)16=-3

(x-18)(x-2)16=-3

Multiply both sides of the equation by 16.

16⋅(x-18)(x-2)16=16⋅-3

Simplify both sides of the equation.

Simplify 16⋅(x-18)(x-2)16.

Cancel the common factor of 16.

Cancel the common factor.

16⋅(x-18)(x-2)16=16⋅-3

Rewrite the expression.

(x-18)(x-2)=16⋅-3

(x-18)(x-2)=16⋅-3

Expand (x-18)(x-2) using the FOIL Method.

Apply the distributive property.

x(x-2)-18(x-2)=16⋅-3

Apply the distributive property.

x⋅x+x⋅-2-18(x-2)=16⋅-3

Apply the distributive property.

x⋅x+x⋅-2-18x-18⋅-2=16⋅-3

x⋅x+x⋅-2-18x-18⋅-2=16⋅-3

Simplify and combine like terms.

Simplify each term.

Multiply x by x.

x2+x⋅-2-18x-18⋅-2=16⋅-3

Move -2 to the left of x.

x2-2⋅x-18x-18⋅-2=16⋅-3

Multiply -18 by -2.

x2-2x-18x+36=16⋅-3

x2-2x-18x+36=16⋅-3

Subtract 18x from -2x.

x2-20x+36=16⋅-3

x2-20x+36=16⋅-3

x2-20x+36=16⋅-3

Multiply 16 by -3.

x2-20x+36=-48

x2-20x+36=-48

Move 48 to the left side of the equation by adding it to both sides.

x2-20x+36+48=0

Add 36 and 48.

x2-20x+84=0

Factor x2-20x+84 using the AC method.

Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is 84 and whose sum is -20.

-14,-6

Write the factored form using these integers.

(x-14)(x-6)=0

(x-14)(x-6)=0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

x-14=0

x-6=0

Set the first factor equal to 0 and solve.

Set the first factor equal to 0.

x-14=0

Add 14 to both sides of the equation.

x=14

x=14

Set the next factor equal to 0 and solve.

Set the next factor equal to 0.

x-6=0

Add 6 to both sides of the equation.

x=6

x=6

The final solution is all the values that make (x-14)(x-6)=0 true.

x=14,6

x=14,6

x=14,6

Solve for x square root of 3x+7- square root of 2x-3=2