0=5(x+2)(x+2)+8x-7

Solution for 0=5(x+2)(x+2)+8x-7 equation:

Simplifying
0 = 5(x + 2)(x + 2) + 8x + -7

Reorder the terms:
0 = 5(2 + x)(x + 2) + 8x + -7

Reorder the terms:
0 = 5(2 + x)(2 + x) + 8x + -7

Multiply (2 + x) * (2 + x)
0 = 5(2(2 + x) + x(2 + x)) + 8x + -7
0 = 5((2 * 2 + x * 2) + x(2 + x)) + 8x + -7
0 = 5((4 + 2x) + x(2 + x)) + 8x + -7
0 = 5(4 + 2x + (2 * x + x * x)) + 8x + -7
0 = 5(4 + 2x + (2x + x2)) + 8x + -7

Combine like terms: 2x + 2x = 4x
0 = 5(4 + 4x + x2) + 8x + -7
0 = (4 * 5 + 4x * 5 + x2 * 5) + 8x + -7
0 = (20 + 20x + 5x2) + 8x + -7

Reorder the terms:
0 = 20 + -7 + 20x + 8x + 5x2

Combine like terms: 20 + -7 = 13
0 = 13 + 20x + 8x + 5x2

Combine like terms: 20x + 8x = 28x
0 = 13 + 28x + 5x2

Solving
0 = 13 + 28x + 5x2

Solving for variable 'x'.

Combine like terms: 0 + -13 = -13
-13 + -28x + -5x2 = 13 + 28x + 5x2 + -13 + -28x + -5x2

Reorder the terms:
-13 + -28x + -5x2 = 13 + -13 + 28x + -28x + 5x2 + -5x2

Combine like terms: 13 + -13 = 0
-13 + -28x + -5x2 = 0 + 28x + -28x + 5x2 + -5x2
-13 + -28x + -5x2 = 28x + -28x + 5x2 + -5x2

Combine like terms: 28x + -28x = 0
-13 + -28x + -5x2 = 0 + 5x2 + -5x2
-13 + -28x + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-13 + -28x + -5x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(13 + 28x + 5x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(13 + 28x + 5x2)' equal to zero and attempt to solve:

Simplifying
13 + 28x + 5x2 = 0

Solving
13 + 28x + 5x2 = 0

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
2.6 + 5.6x + x2 = 0

Move the constant term to the right:

Add '-2.6' to each side of the equation.
2.6 + 5.6x + -2.6 + x2 = 0 + -2.6

Reorder the terms:
2.6 + -2.6 + 5.6x + x2 = 0 + -2.6

Combine like terms: 2.6 + -2.6 = 0.0
0.0 + 5.6x + x2 = 0 + -2.6
5.6x + x2 = 0 + -2.6

Combine like terms: 0 + -2.6 = -2.6
5.6x + x2 = -2.6

The x term is 5.6x.  Take half its coefficient (2.8).
Square it (7.84) and add it to both sides.

Add '7.84' to each side of the equation.
5.6x + 7.84 + x2 = -2.6 + 7.84

Reorder the terms:
7.84 + 5.6x + x2 = -2.6 + 7.84

Combine like terms: -2.6 + 7.84 = 5.24
7.84 + 5.6x + x2 = 5.24

Factor a perfect square on the left side:
(x + 2.8)(x + 2.8) = 5.24

Calculate the square root of the right side: 2.289104628

Break this problem into two subproblems by setting 
(x + 2.8) equal to 2.289104628 and -2.289104628.

Subproblem 1
x + 2.8 = 2.289104628

Simplifying
x + 2.8 = 2.289104628

Reorder the terms:
2.8 + x = 2.289104628

Solving
2.8 + x = 2.289104628

Solving for variable 'x'.

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

Add '-2.8' to each side of the equation.
2.8 + -2.8 + x = 2.289104628 + -2.8

Combine like terms: 2.8 + -2.8 = 0.0
0.0 + x = 2.289104628 + -2.8
x = 2.289104628 + -2.8

Combine like terms: 2.289104628 + -2.8 = -0.510895372
x = -0.510895372

Simplifying
x = -0.510895372

Subproblem 2
x + 2.8 = -2.289104628

Simplifying
x + 2.8 = -2.289104628

Reorder the terms:
2.8 + x = -2.289104628

Solving
2.8 + x = -2.289104628

Solving for variable 'x'.

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

Add '-2.8' to each side of the equation.
2.8 + -2.8 + x = -2.289104628 + -2.8

Combine like terms: 2.8 + -2.8 = 0.0
0.0 + x = -2.289104628 + -2.8
x = -2.289104628 + -2.8

Combine like terms: -2.289104628 + -2.8 = -5.089104628
x = -5.089104628

Simplifying
x = -5.089104628

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.510895372, -5.089104628}
Solution
x = {-0.510895372, -5.089104628}