4x^2+64x-140=0

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Solution for 4x^2+64x-140=0 equation: 


Simplifying
4x2 + 64x + -140 = 0

Reorder the terms:
-140 + 64x + 4x2 = 0

Solving
-140 + 64x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-35 + 16x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-35 + 16x + x2)' equal to zero and attempt to solve:

Simplifying
-35 + 16x + x2 = 0

Solving
-35 + 16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '35' to each side of the equation.
-35 + 16x + 35 + x2 = 0 + 35

Reorder the terms:
-35 + 35 + 16x + x2 = 0 + 35

Combine like terms: -35 + 35 = 0
0 + 16x + x2 = 0 + 35
16x + x2 = 0 + 35

Combine like terms: 0 + 35 = 35
16x + x2 = 35

The x term is 16x.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16x + 64 + x2 = 35 + 64

Reorder the terms:
64 + 16x + x2 = 35 + 64

Combine like terms: 35 + 64 = 99
64 + 16x + x2 = 99

Factor a perfect square on the left side:
(x + 8)(x + 8) = 99

Calculate the square root of the right side: 9.949874371

Break this problem into two subproblems by setting 
(x + 8) equal to 9.949874371 and -9.949874371.


Subproblem 1
x + 8 = 9.949874371

Simplifying
x + 8 = 9.949874371

Reorder the terms:
8 + x = 9.949874371

Solving
8 + x = 9.949874371

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x = 9.949874371 + -8

Combine like terms: 8 + -8 = 0
0 + x = 9.949874371 + -8
x = 9.949874371 + -8

Combine like terms: 9.949874371 + -8 = 1.949874371
x = 1.949874371

Simplifying
x = 1.949874371


Subproblem 2
x + 8 = -9.949874371

Simplifying
x + 8 = -9.949874371

Reorder the terms:
8 + x = -9.949874371

Solving
8 + x = -9.949874371

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x = -9.949874371 + -8

Combine like terms: 8 + -8 = 0
0 + x = -9.949874371 + -8
x = -9.949874371 + -8

Combine like terms: -9.949874371 + -8 = -17.949874371
x = -17.949874371

Simplifying
x = -17.949874371


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.949874371, -17.949874371}
Solution
x = {1.949874371, -17.949874371}

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