-4x^2-700x+15000=0

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Solution for -4x^2-700x+15000=0 equation: 


Simplifying
-4x2 + -700x + 15000 = 0

Reorder the terms:
15000 + -700x + -4x2 = 0

Solving
15000 + -700x + -4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(3750 + -175x + -1x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(3750 + -175x + -1x2)' equal to zero and attempt to solve:

Simplifying
3750 + -175x + -1x2 = 0

Solving
3750 + -175x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-3750 + 175x + x2 = 0

Move the constant term to the right:

Add '3750' to each side of the equation.
-3750 + 175x + 3750 + x2 = 0 + 3750

Reorder the terms:
-3750 + 3750 + 175x + x2 = 0 + 3750

Combine like terms: -3750 + 3750 = 0
0 + 175x + x2 = 0 + 3750
175x + x2 = 0 + 3750

Combine like terms: 0 + 3750 = 3750
175x + x2 = 3750

The x term is 175x.  Take half its coefficient (87.5).
Square it (7656.25) and add it to both sides.

Add '7656.25' to each side of the equation.
175x + 7656.25 + x2 = 3750 + 7656.25

Reorder the terms:
7656.25 + 175x + x2 = 3750 + 7656.25

Combine like terms: 3750 + 7656.25 = 11406.25
7656.25 + 175x + x2 = 11406.25

Factor a perfect square on the left side:
(x + 87.5)(x + 87.5) = 11406.25

Calculate the square root of the right side: 106.800046816

Break this problem into two subproblems by setting 
(x + 87.5) equal to 106.800046816 and -106.800046816.


Subproblem 1
x + 87.5 = 106.800046816

Simplifying
x + 87.5 = 106.800046816

Reorder the terms:
87.5 + x = 106.800046816

Solving
87.5 + x = 106.800046816

Solving for variable 'x'.

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

Add '-87.5' to each side of the equation.
87.5 + -87.5 + x = 106.800046816 + -87.5

Combine like terms: 87.5 + -87.5 = 0.0
0.0 + x = 106.800046816 + -87.5
x = 106.800046816 + -87.5

Combine like terms: 106.800046816 + -87.5 = 19.300046816
x = 19.300046816

Simplifying
x = 19.300046816


Subproblem 2
x + 87.5 = -106.800046816

Simplifying
x + 87.5 = -106.800046816

Reorder the terms:
87.5 + x = -106.800046816

Solving
87.5 + x = -106.800046816

Solving for variable 'x'.

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

Add '-87.5' to each side of the equation.
87.5 + -87.5 + x = -106.800046816 + -87.5

Combine like terms: 87.5 + -87.5 = 0.0
0.0 + x = -106.800046816 + -87.5
x = -106.800046816 + -87.5

Combine like terms: -106.800046816 + -87.5 = -194.300046816
x = -194.300046816

Simplifying
x = -194.300046816


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {19.300046816, -194.300046816}
Solution
x = {19.300046816, -194.300046816}

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