8x^2+50x-100=0

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Solution for 8x^2+50x-100=0 equation: 


Simplifying
8x2 + 50x + -100 = 0

Reorder the terms:
-100 + 50x + 8x2 = 0

Solving
-100 + 50x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-50 + 25x + 4x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-50 + 25x + 4x2)' equal to zero and attempt to solve:

Simplifying
-50 + 25x + 4x2 = 0

Solving
-50 + 25x + 4x2 = 0

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

Divide each side by '4'.
-12.5 + 6.25x + x2 = 0

Move the constant term to the right:

Add '12.5' to each side of the equation.
-12.5 + 6.25x + 12.5 + x2 = 0 + 12.5

Reorder the terms:
-12.5 + 12.5 + 6.25x + x2 = 0 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + 6.25x + x2 = 0 + 12.5
6.25x + x2 = 0 + 12.5

Combine like terms: 0 + 12.5 = 12.5
6.25x + x2 = 12.5

The x term is 6.25x.  Take half its coefficient (3.125).
Square it (9.765625) and add it to both sides.

Add '9.765625' to each side of the equation.
6.25x + 9.765625 + x2 = 12.5 + 9.765625

Reorder the terms:
9.765625 + 6.25x + x2 = 12.5 + 9.765625

Combine like terms: 12.5 + 9.765625 = 22.265625
9.765625 + 6.25x + x2 = 22.265625

Factor a perfect square on the left side:
(x + 3.125)(x + 3.125) = 22.265625

Calculate the square root of the right side: 4.718646522

Break this problem into two subproblems by setting 
(x + 3.125) equal to 4.718646522 and -4.718646522.


Subproblem 1
x + 3.125 = 4.718646522

Simplifying
x + 3.125 = 4.718646522

Reorder the terms:
3.125 + x = 4.718646522

Solving
3.125 + x = 4.718646522

Solving for variable 'x'.

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

Add '-3.125' to each side of the equation.
3.125 + -3.125 + x = 4.718646522 + -3.125

Combine like terms: 3.125 + -3.125 = 0.000
0.000 + x = 4.718646522 + -3.125
x = 4.718646522 + -3.125

Combine like terms: 4.718646522 + -3.125 = 1.593646522
x = 1.593646522

Simplifying
x = 1.593646522


Subproblem 2
x + 3.125 = -4.718646522

Simplifying
x + 3.125 = -4.718646522

Reorder the terms:
3.125 + x = -4.718646522

Solving
3.125 + x = -4.718646522

Solving for variable 'x'.

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

Add '-3.125' to each side of the equation.
3.125 + -3.125 + x = -4.718646522 + -3.125

Combine like terms: 3.125 + -3.125 = 0.000
0.000 + x = -4.718646522 + -3.125
x = -4.718646522 + -3.125

Combine like terms: -4.718646522 + -3.125 = -7.843646522
x = -7.843646522

Simplifying
x = -7.843646522


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.593646522, -7.843646522}
Solution
x = {1.593646522, -7.843646522}

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