25x^2+200x-100=0

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Solution for 25x^2+200x-100=0 equation: 


Simplifying
25x2 + 200x + -100 = 0

Reorder the terms:
-100 + 200x + 25x2 = 0

Solving
-100 + 200x + 25x2 = 0

Solving for variable 'x'.

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

Ignore the factor 25.

Subproblem 1
Set the factor '(-4 + 8x + x2)' equal to zero and attempt to solve:

Simplifying
-4 + 8x + x2 = 0

Solving
-4 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 8x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + 8x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 8x + x2 = 0 + 4
8x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
8x + x2 = 4

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = 4 + 16

Reorder the terms:
16 + 8x + x2 = 4 + 16

Combine like terms: 4 + 16 = 20
16 + 8x + x2 = 20

Factor a perfect square on the left side:
(x + 4)(x + 4) = 20

Calculate the square root of the right side: 4.472135955

Break this problem into two subproblems by setting 
(x + 4) equal to 4.472135955 and -4.472135955.


Subproblem 1
x + 4 = 4.472135955

Simplifying
x + 4 = 4.472135955

Reorder the terms:
4 + x = 4.472135955

Solving
4 + x = 4.472135955

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = 4.472135955 + -4

Combine like terms: 4 + -4 = 0
0 + x = 4.472135955 + -4
x = 4.472135955 + -4

Combine like terms: 4.472135955 + -4 = 0.472135955
x = 0.472135955

Simplifying
x = 0.472135955


Subproblem 2
x + 4 = -4.472135955

Simplifying
x + 4 = -4.472135955

Reorder the terms:
4 + x = -4.472135955

Solving
4 + x = -4.472135955

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = -4.472135955 + -4

Combine like terms: 4 + -4 = 0
0 + x = -4.472135955 + -4
x = -4.472135955 + -4

Combine like terms: -4.472135955 + -4 = -8.472135955
x = -8.472135955

Simplifying
x = -8.472135955


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.472135955, -8.472135955}
Solution
x = {0.472135955, -8.472135955}

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