x^2+(x+4)(x+4)=170

Solution for x^2+(x+4)(x+4)=170 equation:

Simplifying
x2 + (x + 4)(x + 4) = 170

Reorder the terms:
x2 + (4 + x)(x + 4) = 170

Reorder the terms:
x2 + (4 + x)(4 + x) = 170

Multiply (4 + x) * (4 + x)
x2 + (4(4 + x) + x(4 + x)) = 170
x2 + ((4 * 4 + x * 4) + x(4 + x)) = 170
x2 + ((16 + 4x) + x(4 + x)) = 170
x2 + (16 + 4x + (4 * x + x * x)) = 170
x2 + (16 + 4x + (4x + x2)) = 170

Combine like terms: 4x + 4x = 8x
x2 + (16 + 8x + x2) = 170

Reorder the terms:
16 + 8x + x2 + x2 = 170

Combine like terms: x2 + x2 = 2x2
16 + 8x + 2x2 = 170

Solving
16 + 8x + 2x2 = 170

Solving for variable 'x'.

Reorder the terms:
16 + -170 + 8x + 2x2 = 170 + -170

Combine like terms: 16 + -170 = -154
-154 + 8x + 2x2 = 170 + -170

Combine like terms: 170 + -170 = 0
-154 + 8x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-77 + 4x + x2) = 0

Factor a trinomial.
2((-11 + -1x)(7 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-11 + -1x)' equal to zero and attempt to solve:

Simplifying
-11 + -1x = 0

Solving
-11 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '11' to each side of the equation.
-11 + 11 + -1x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -1x = 0 + 11
-1x = 0 + 11

Combine like terms: 0 + 11 = 11
-1x = 11

Divide each side by '-1'.
x = -11

Simplifying
x = -11
Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-11, 7}