50(x^2+x-100)=0

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


Simplifying
50(x2 + x + -100) = 0

Reorder the terms:
50(-100 + x + x2) = 0
(-100 * 50 + x * 50 + x2 * 50) = 0
(-5000 + 50x + 50x2) = 0

Solving
-5000 + 50x + 50x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '50'.
50(-100 + x + x2) = 0

Ignore the factor 50.

Subproblem 1
Set the factor '(-100 + x + x2)' equal to zero and attempt to solve:

Simplifying
-100 + x + x2 = 0

Solving
-100 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '100' to each side of the equation.
-100 + x + 100 + x2 = 0 + 100

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

Combine like terms: -100 + 100 = 0
0 + x + x2 = 0 + 100
x + x2 = 0 + 100

Combine like terms: 0 + 100 = 100
x + x2 = 100

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = 100 + 0.25

Reorder the terms:
0.25 + x + x2 = 100 + 0.25

Combine like terms: 100 + 0.25 = 100.25
0.25 + x + x2 = 100.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 100.25

Calculate the square root of the right side: 10.012492197

Break this problem into two subproblems by setting 
(x + 0.5) equal to 10.012492197 and -10.012492197.


Subproblem 1
x + 0.5 = 10.012492197

Simplifying
x + 0.5 = 10.012492197

Reorder the terms:
0.5 + x = 10.012492197

Solving
0.5 + x = 10.012492197

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 10.012492197 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 10.012492197 + -0.5
x = 10.012492197 + -0.5

Combine like terms: 10.012492197 + -0.5 = 9.512492197
x = 9.512492197

Simplifying
x = 9.512492197


Subproblem 2
x + 0.5 = -10.012492197

Simplifying
x + 0.5 = -10.012492197

Reorder the terms:
0.5 + x = -10.012492197

Solving
0.5 + x = -10.012492197

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -10.012492197 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -10.012492197 + -0.5
x = -10.012492197 + -0.5

Combine like terms: -10.012492197 + -0.5 = -10.512492197
x = -10.512492197

Simplifying
x = -10.512492197


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.512492197, -10.512492197}
Solution
x = {9.512492197, -10.512492197}

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