4x^2+100x-32=0

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Solution for 4x^2+100x-32=0 equation: 


Simplifying
4x2 + 100x + -32 = 0

Reorder the terms:
-32 + 100x + 4x2 = 0

Solving
-32 + 100x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-8 + 25x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-8 + 25x + x2)' equal to zero and attempt to solve:

Simplifying
-8 + 25x + x2 = 0

Solving
-8 + 25x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + 25x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + 25x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 25x + x2 = 0 + 8
25x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
25x + x2 = 8

The x term is 25x.  Take half its coefficient (12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
25x + 156.25 + x2 = 8 + 156.25

Reorder the terms:
156.25 + 25x + x2 = 8 + 156.25

Combine like terms: 8 + 156.25 = 164.25
156.25 + 25x + x2 = 164.25

Factor a perfect square on the left side:
(x + 12.5)(x + 12.5) = 164.25

Calculate the square root of the right side: 12.816005618

Break this problem into two subproblems by setting 
(x + 12.5) equal to 12.816005618 and -12.816005618.


Subproblem 1
x + 12.5 = 12.816005618

Simplifying
x + 12.5 = 12.816005618

Reorder the terms:
12.5 + x = 12.816005618

Solving
12.5 + x = 12.816005618

Solving for variable 'x'.

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

Add '-12.5' to each side of the equation.
12.5 + -12.5 + x = 12.816005618 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + x = 12.816005618 + -12.5
x = 12.816005618 + -12.5

Combine like terms: 12.816005618 + -12.5 = 0.316005618
x = 0.316005618

Simplifying
x = 0.316005618


Subproblem 2
x + 12.5 = -12.816005618

Simplifying
x + 12.5 = -12.816005618

Reorder the terms:
12.5 + x = -12.816005618

Solving
12.5 + x = -12.816005618

Solving for variable 'x'.

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

Add '-12.5' to each side of the equation.
12.5 + -12.5 + x = -12.816005618 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + x = -12.816005618 + -12.5
x = -12.816005618 + -12.5

Combine like terms: -12.816005618 + -12.5 = -25.316005618
x = -25.316005618

Simplifying
x = -25.316005618


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.316005618, -25.316005618}
Solution
x = {0.316005618, -25.316005618}

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