25x^2+100x-1600=0

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Solution for 25x^2+100x-1600=0 equation: 


Simplifying
25x2 + 100x + -1600 = 0

Reorder the terms:
-1600 + 100x + 25x2 = 0

Solving
-1600 + 100x + 25x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '25'.
25(-64 + 4x + x2) = 0

Ignore the factor 25.

Subproblem 1
Set the factor '(-64 + 4x + x2)' equal to zero and attempt to solve:

Simplifying
-64 + 4x + x2 = 0

Solving
-64 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '64' to each side of the equation.
-64 + 4x + 64 + x2 = 0 + 64

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

Combine like terms: -64 + 64 = 0
0 + 4x + x2 = 0 + 64
4x + x2 = 0 + 64

Combine like terms: 0 + 64 = 64
4x + x2 = 64

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 64 + 4

Reorder the terms:
4 + 4x + x2 = 64 + 4

Combine like terms: 64 + 4 = 68
4 + 4x + x2 = 68

Factor a perfect square on the left side:
(x + 2)(x + 2) = 68

Calculate the square root of the right side: 8.246211251

Break this problem into two subproblems by setting 
(x + 2) equal to 8.246211251 and -8.246211251.


Subproblem 1
x + 2 = 8.246211251

Simplifying
x + 2 = 8.246211251

Reorder the terms:
2 + x = 8.246211251

Solving
2 + x = 8.246211251

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 8.246211251 + -2

Combine like terms: 2 + -2 = 0
0 + x = 8.246211251 + -2
x = 8.246211251 + -2

Combine like terms: 8.246211251 + -2 = 6.246211251
x = 6.246211251

Simplifying
x = 6.246211251


Subproblem 2
x + 2 = -8.246211251

Simplifying
x + 2 = -8.246211251

Reorder the terms:
2 + x = -8.246211251

Solving
2 + x = -8.246211251

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -8.246211251 + -2

Combine like terms: 2 + -2 = 0
0 + x = -8.246211251 + -2
x = -8.246211251 + -2

Combine like terms: -8.246211251 + -2 = -10.246211251
x = -10.246211251

Simplifying
x = -10.246211251


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.246211251, -10.246211251}
Solution
x = {6.246211251, -10.246211251}

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