8x^2+40x-140=0

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Solution for 8x^2+40x-140=0 equation: 


Simplifying
8x2 + 40x + -140 = 0

Reorder the terms:
-140 + 40x + 8x2 = 0

Solving
-140 + 40x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-35 + 10x + 2x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-35 + 10x + 2x2)' equal to zero and attempt to solve:

Simplifying
-35 + 10x + 2x2 = 0

Solving
-35 + 10x + 2x2 = 0

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

Divide each side by '2'.
-17.5 + 5x + x2 = 0

Move the constant term to the right:

Add '17.5' to each side of the equation.
-17.5 + 5x + 17.5 + x2 = 0 + 17.5

Reorder the terms:
-17.5 + 17.5 + 5x + x2 = 0 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + 5x + x2 = 0 + 17.5
5x + x2 = 0 + 17.5

Combine like terms: 0 + 17.5 = 17.5
5x + x2 = 17.5

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 17.5 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 17.5 + 6.25

Combine like terms: 17.5 + 6.25 = 23.75
6.25 + 5x + x2 = 23.75

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 23.75

Calculate the square root of the right side: 4.873397172

Break this problem into two subproblems by setting 
(x + 2.5) equal to 4.873397172 and -4.873397172.


Subproblem 1
x + 2.5 = 4.873397172

Simplifying
x + 2.5 = 4.873397172

Reorder the terms:
2.5 + x = 4.873397172

Solving
2.5 + x = 4.873397172

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 4.873397172 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 4.873397172 + -2.5
x = 4.873397172 + -2.5

Combine like terms: 4.873397172 + -2.5 = 2.373397172
x = 2.373397172

Simplifying
x = 2.373397172


Subproblem 2
x + 2.5 = -4.873397172

Simplifying
x + 2.5 = -4.873397172

Reorder the terms:
2.5 + x = -4.873397172

Solving
2.5 + x = -4.873397172

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -4.873397172 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -4.873397172 + -2.5
x = -4.873397172 + -2.5

Combine like terms: -4.873397172 + -2.5 = -7.373397172
x = -7.373397172

Simplifying
x = -7.373397172


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.373397172, -7.373397172}
Solution
x = {2.373397172, -7.373397172}

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