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

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 by -8 and simplify.
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
Simplify the right side of the equation.
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
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
The complete solution is the result of both the positive and negative portions of the solution.
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