25x^2+200x-400=0

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Solution for 25x^2+200x-400=0 equation: 


Simplifying
25x2 + 200x + -400 = 0

Reorder the terms:
-400 + 200x + 25x2 = 0

Solving
-400 + 200x + 25x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '25'.
25(-16 + 8x + x2) = 0

Ignore the factor 25.

Subproblem 1
Set the factor '(-16 + 8x + x2)' equal to zero and attempt to solve:

Simplifying
-16 + 8x + x2 = 0

Solving
-16 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 8x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + 8x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 8x + x2 = 0 + 16
8x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
8x + x2 = 16

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 = 16 + 16

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

Combine like terms: 16 + 16 = 32
16 + 8x + x2 = 32

Factor a perfect square on the left side:
(x + 4)(x + 4) = 32

Calculate the square root of the right side: 5.656854249

Break this problem into two subproblems by setting 
(x + 4) equal to 5.656854249 and -5.656854249.


Subproblem 1
x + 4 = 5.656854249

Simplifying
x + 4 = 5.656854249

Reorder the terms:
4 + x = 5.656854249

Solving
4 + x = 5.656854249

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 = 5.656854249 + -4

Combine like terms: 4 + -4 = 0
0 + x = 5.656854249 + -4
x = 5.656854249 + -4

Combine like terms: 5.656854249 + -4 = 1.656854249
x = 1.656854249

Simplifying
x = 1.656854249


Subproblem 2
x + 4 = -5.656854249

Simplifying
x + 4 = -5.656854249

Reorder the terms:
4 + x = -5.656854249

Solving
4 + x = -5.656854249

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 = -5.656854249 + -4

Combine like terms: 4 + -4 = 0
0 + x = -5.656854249 + -4
x = -5.656854249 + -4

Combine like terms: -5.656854249 + -4 = -9.656854249
x = -9.656854249

Simplifying
x = -9.656854249


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.656854249, -9.656854249}
Solution
x = {1.656854249, -9.656854249}

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