8x(-7-5x)+10=-18

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Solution for 8x(-7-5x)+10=-18 equation: 


Simplifying
8x(-7 + -5x) + 10 = -18
(-7 * 8x + -5x * 8x) + 10 = -18
(-56x + -40x2) + 10 = -18

Reorder the terms:
10 + -56x + -40x2 = -18

Solving
10 + -56x + -40x2 = -18

Solving for variable 'x'.

Reorder the terms:
10 + 18 + -56x + -40x2 = -18 + 18

Combine like terms: 10 + 18 = 28
28 + -56x + -40x2 = -18 + 18

Combine like terms: -18 + 18 = 0
28 + -56x + -40x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(7 + -14x + -10x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(7 + -14x + -10x2)' equal to zero and attempt to solve:

Simplifying
7 + -14x + -10x2 = 0

Solving
7 + -14x + -10x2 = 0

Begin completing the square.  Divide all terms by
-10 the coefficient of the squared term: 

Divide each side by '-10'.
-0.7 + 1.4x + x2 = 0.0

Move the constant term to the right:

Add '0.7' to each side of the equation.
-0.7 + 1.4x + 0.7 + x2 = 0.0 + 0.7

Reorder the terms:
-0.7 + 0.7 + 1.4x + x2 = 0.0 + 0.7

Combine like terms: -0.7 + 0.7 = 0.0
0.0 + 1.4x + x2 = 0.0 + 0.7
1.4x + x2 = 0.0 + 0.7

Combine like terms: 0.0 + 0.7 = 0.7
1.4x + x2 = 0.7

The x term is 1.4x.  Take half its coefficient (0.7).
Square it (0.49) and add it to both sides.

Add '0.49' to each side of the equation.
1.4x + 0.49 + x2 = 0.7 + 0.49

Reorder the terms:
0.49 + 1.4x + x2 = 0.7 + 0.49

Combine like terms: 0.7 + 0.49 = 1.19
0.49 + 1.4x + x2 = 1.19

Factor a perfect square on the left side:
(x + 0.7)(x + 0.7) = 1.19

Calculate the square root of the right side: 1.090871211

Break this problem into two subproblems by setting 
(x + 0.7) equal to 1.090871211 and -1.090871211.


Subproblem 1
x + 0.7 = 1.090871211

Simplifying
x + 0.7 = 1.090871211

Reorder the terms:
0.7 + x = 1.090871211

Solving
0.7 + x = 1.090871211

Solving for variable 'x'.

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

Add '-0.7' to each side of the equation.
0.7 + -0.7 + x = 1.090871211 + -0.7

Combine like terms: 0.7 + -0.7 = 0.0
0.0 + x = 1.090871211 + -0.7
x = 1.090871211 + -0.7

Combine like terms: 1.090871211 + -0.7 = 0.390871211
x = 0.390871211

Simplifying
x = 0.390871211


Subproblem 2
x + 0.7 = -1.090871211

Simplifying
x + 0.7 = -1.090871211

Reorder the terms:
0.7 + x = -1.090871211

Solving
0.7 + x = -1.090871211

Solving for variable 'x'.

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

Add '-0.7' to each side of the equation.
0.7 + -0.7 + x = -1.090871211 + -0.7

Combine like terms: 0.7 + -0.7 = 0.0
0.0 + x = -1.090871211 + -0.7
x = -1.090871211 + -0.7

Combine like terms: -1.090871211 + -0.7 = -1.790871211
x = -1.790871211

Simplifying
x = -1.790871211


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.390871211, -1.790871211}
Solution
x = {0.390871211, -1.790871211}

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