2x^2+10x-936=0

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Solution for 2x^2+10x-936=0 equation: 


Simplifying
2x2 + 10x + -936 = 0

Reorder the terms:
-936 + 10x + 2x2 = 0

Solving
-936 + 10x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-468 + 5x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-468 + 5x + x2)' equal to zero and attempt to solve:

Simplifying
-468 + 5x + x2 = 0

Solving
-468 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '468' to each side of the equation.
-468 + 5x + 468 + x2 = 0 + 468

Reorder the terms:
-468 + 468 + 5x + x2 = 0 + 468

Combine like terms: -468 + 468 = 0
0 + 5x + x2 = 0 + 468
5x + x2 = 0 + 468

Combine like terms: 0 + 468 = 468
5x + x2 = 468

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 468 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 468 + 6.25

Combine like terms: 468 + 6.25 = 474.25
6.25 + 5x + x2 = 474.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 474.25

Calculate the square root of the right side: 21.77728174

Break this problem into two subproblems by setting 
(x + 2.5) equal to 21.77728174 and -21.77728174.


Subproblem 1
x + 2.5 = 21.77728174

Simplifying
x + 2.5 = 21.77728174

Reorder the terms:
2.5 + x = 21.77728174

Solving
2.5 + x = 21.77728174

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 21.77728174 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 21.77728174 + -2.5
x = 21.77728174 + -2.5

Combine like terms: 21.77728174 + -2.5 = 19.27728174
x = 19.27728174

Simplifying
x = 19.27728174


Subproblem 2
x + 2.5 = -21.77728174

Simplifying
x + 2.5 = -21.77728174

Reorder the terms:
2.5 + x = -21.77728174

Solving
2.5 + x = -21.77728174

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -21.77728174 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -21.77728174 + -2.5
x = -21.77728174 + -2.5

Combine like terms: -21.77728174 + -2.5 = -24.27728174
x = -24.27728174

Simplifying
x = -24.27728174


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {19.27728174, -24.27728174}
Solution
x = {19.27728174, -24.27728174}

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