15(x+4)2-23(x+4)2=-4

Subtract 23(x+4)2 from 15(x+4)2.

-8(x+4)2=-4

Divide each term in -8(x+4)2=-4 by -8.

-8(x+4)2-8=-4-8

Cancel the common factor of -8.

Cancel the common factor.

-8(x+4)2-8=-4-8

Divide (x+4)2 by 1.

(x+4)2=-4-8

(x+4)2=-4-8

Cancel the common factor of -4 and -8.

Factor -4 out of -4.

(x+4)2=-4(1)-8

Cancel the common factors.

Factor -4 out of -8.

(x+4)2=-4⋅1-4⋅2

Cancel the common factor.

(x+4)2=-4⋅1-4⋅2

Rewrite the expression.

(x+4)2=12

(x+4)2=12

(x+4)2=12

(x+4)2=12

Take the square root of each side of the equation to set up the solution for x

(x+4)2⋅12=±12

Remove the perfect root factor x+4 under the radical to solve for x.

x+4=±12

Rewrite 12 as 12.

x+4=±12

Any root of 1 is 1.

x+4=±12

Multiply 12 by 22.

x+4=±12⋅22

Combine and simplify the denominator.

Multiply 12 and 22.

x+4=±222

Raise 2 to the power of 1.

x+4=±222

Raise 2 to the power of 1.

x+4=±222

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

x+4=±221+1

Add 1 and 1.

x+4=±222

Rewrite 22 as 2.

Use axn=axn to rewrite 2 as 212.

x+4=±2(212)2

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

x+4=±2212⋅2

Combine 12 and 2.

x+4=±2222

Cancel the common factor of 2.

Cancel the common factor.

x+4=±2222

Divide 1 by 1.

x+4=±22

x+4=±22

Evaluate the exponent.

x+4=±22

x+4=±22

x+4=±22

x+4=±22

First, use the positive value of the ± to find the first solution.

x+4=22

Subtract 4 from both sides of the equation.

x=22-4

Next, use the negative value of the ± to find the second solution.

x+4=-22

Subtract 4 from both sides of the equation.

x=-22-4

The complete solution is the result of both the positive and negative portions of the solution.

x=22-4,-22-4

x=22-4,-22-4

The result can be shown in multiple forms.

Exact Form:

x=22-4,-22-4

Decimal Form:

x=-3.29289321…,-4.70710678…

Solve Using the Square Root Property 15(x+4)^2-23(x+4)^2=-4