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

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
Simplify each side of the equation.
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
Solve for x.
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
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
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
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
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
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