5x-12-x-3=-1

Add x to both sides of the equation.

5x-12-3=-1+x

Add 3 to both sides of the equation.

5x-12=-1+x+3

Add -1 and 3.

5x-12=x+2

5x-12=x+2

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

5x-122=(x+2)2

Multiply the exponents in ((5x-12)12)2.

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

(5x-12)12⋅2=(x+2)2

Cancel the common factor of 2.

Cancel the common factor.

(5x-12)12⋅2=(x+2)2

Rewrite the expression.

(5x-12)1=(x+2)2

(5x-12)1=(x+2)2

(5x-12)1=(x+2)2

Simplify.

5x-12=(x+2)2

5x-12=(x+2)2

Simplify (x+2)2.

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

5x-12=(x+2)(x+2)

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

Apply the distributive property.

5x-12=x(x+2)+2(x+2)

Apply the distributive property.

5x-12=xx+x⋅2+2(x+2)

Apply the distributive property.

5x-12=xx+x⋅2+2x+2⋅2

5x-12=xx+x⋅2+2x+2⋅2

Simplify and combine like terms.

Simplify each term.

Multiply xx.

Raise x to the power of 1.

5x-12=x1x+x⋅2+2x+2⋅2

Raise x to the power of 1.

5x-12=x1x1+x⋅2+2x+2⋅2

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

5x-12=x1+1+x⋅2+2x+2⋅2

Add 1 and 1.

5x-12=x2+x⋅2+2x+2⋅2

5x-12=x2+x⋅2+2x+2⋅2

Rewrite x2 as x.

Use axn=axn to rewrite x as x12.

5x-12=(x12)2+x⋅2+2x+2⋅2

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

5x-12=x12⋅2+x⋅2+2x+2⋅2

Combine 12 and 2.

5x-12=x22+x⋅2+2x+2⋅2

Cancel the common factor of 2.

Cancel the common factor.

5x-12=x22+x⋅2+2x+2⋅2

Divide 1 by 1.

5x-12=x1+x⋅2+2x+2⋅2

5x-12=x1+x⋅2+2x+2⋅2

Simplify.

5x-12=x+x⋅2+2x+2⋅2

5x-12=x+x⋅2+2x+2⋅2

Move 2 to the left of x.

5x-12=x+2⋅x+2x+2⋅2

Multiply 2 by 2.

5x-12=x+2x+2x+4

5x-12=x+2x+2x+4

Add 2x and 2x.

5x-12=x+4x+4

5x-12=x+4x+4

5x-12=x+4x+4

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

x+4x+4=5x-12

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

Subtract x from both sides of the equation.

4x+4=5x-12-x

Subtract 4 from both sides of the equation.

4x=5x-12-x-4

Subtract x from 5x.

4x=4x-12-4

Subtract 4 from -12.

4x=4x-16

4x=4x-16

Divide each term by 4 and simplify.

Divide each term in 4x=4x-16 by 4.

4×4=4×4+-164

Cancel the common factor of 4.

Cancel the common factor.

4×4=4×4+-164

Divide x by 1.

x=4×4+-164

x=4×4+-164

Simplify each term.

Cancel the common factor of 4.

Cancel the common factor.

x=4×4+-164

Divide x by 1.

x=x+-164

x=x+-164

Divide -16 by 4.

x=x-4

x=x-4

x=x-4

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

x2=(x-4)2

Simplify each side of the equation.

Multiply the exponents in (x12)2.

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

x12⋅2=(x-4)2

Cancel the common factor of 2.

Cancel the common factor.

x12⋅2=(x-4)2

Rewrite the expression.

x1=(x-4)2

x1=(x-4)2

x1=(x-4)2

Simplify.

x=(x-4)2

x=(x-4)2

Solve for x.

Simplify (x-4)2.

Rewrite (x-4)2 as (x-4)(x-4).

x=(x-4)(x-4)

Expand (x-4)(x-4) using the FOIL Method.

Apply the distributive property.

x=x(x-4)-4(x-4)

Apply the distributive property.

x=x⋅x+x⋅-4-4(x-4)

Apply the distributive property.

x=x⋅x+x⋅-4-4x-4⋅-4

x=x⋅x+x⋅-4-4x-4⋅-4

Simplify and combine like terms.

Simplify each term.

Multiply x by x.

x=x2+x⋅-4-4x-4⋅-4

Move -4 to the left of x.

x=x2-4⋅x-4x-4⋅-4

Multiply -4 by -4.

x=x2-4x-4x+16

x=x2-4x-4x+16

Subtract 4x from -4x.

x=x2-8x+16

x=x2-8x+16

x=x2-8x+16

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

x2-8x+16=x

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

Subtract x from both sides of the equation.

x2-8x+16-x=0

Subtract x from -8x.

x2-9x+16=0

x2-9x+16=0

Use the quadratic formula to find the solutions.

-b±b2-4(ac)2a

Substitute the values a=1, b=-9, and c=16 into the quadratic formula and solve for x.

9±(-9)2-4⋅(1⋅16)2⋅1

Simplify.

Simplify the numerator.

Raise -9 to the power of 2.

x=9±81-4⋅(1⋅16)2⋅1

Multiply 16 by 1.

x=9±81-4⋅162⋅1

Multiply -4 by 16.

x=9±81-642⋅1

Subtract 64 from 81.

x=9±172⋅1

x=9±172⋅1

Multiply 2 by 1.

x=9±172

x=9±172

Simplify the expression to solve for the + portion of the ±.

Simplify the numerator.

Raise -9 to the power of 2.

x=9±81-4⋅(1⋅16)2⋅1

Multiply 16 by 1.

x=9±81-4⋅162⋅1

Multiply -4 by 16.

x=9±81-642⋅1

Subtract 64 from 81.

x=9±172⋅1

x=9±172⋅1

Multiply 2 by 1.

x=9±172

Change the ± to +.

x=9+172

x=9+172

Simplify the expression to solve for the – portion of the ±.

Simplify the numerator.

Raise -9 to the power of 2.

x=9±81-4⋅(1⋅16)2⋅1

Multiply 16 by 1.

x=9±81-4⋅162⋅1

Multiply -4 by 16.

x=9±81-642⋅1

Subtract 64 from 81.

x=9±172⋅1

x=9±172⋅1

Multiply 2 by 1.

x=9±172

Change the ± to -.

x=9-172

x=9-172

The final answer is the combination of both solutions.

x=9+172,9-172

x=9+172,9-172

x=9+172,9-172

Exclude the solutions that do not make 5x-12-x-3=-1 true.

x=9+172

The result can be shown in multiple forms.

Exact Form:

x=9+172

Decimal Form:

x=6.56155281…

Solve using the Square Root Property square root of 5x-12- square root of x-3=-1