2x^2+10x-816=0

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Solution for 2x^2+10x-816=0 equation: 


Simplifying
2x2 + 10x + -816 = 0

Reorder the terms:
-816 + 10x + 2x2 = 0

Solving
-816 + 10x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-408 + 5x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-408 + 5x + x2)' equal to zero and attempt to solve:

Simplifying
-408 + 5x + x2 = 0

Solving
-408 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '408' to each side of the equation.
-408 + 5x + 408 + x2 = 0 + 408

Reorder the terms:
-408 + 408 + 5x + x2 = 0 + 408

Combine like terms: -408 + 408 = 0
0 + 5x + x2 = 0 + 408
5x + x2 = 0 + 408

Combine like terms: 0 + 408 = 408
5x + x2 = 408

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 = 408 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 408 + 6.25

Combine like terms: 408 + 6.25 = 414.25
6.25 + 5x + x2 = 414.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 414.25

Calculate the square root of the right side: 20.353132437

Break this problem into two subproblems by setting 
(x + 2.5) equal to 20.353132437 and -20.353132437.


Subproblem 1
x + 2.5 = 20.353132437

Simplifying
x + 2.5 = 20.353132437

Reorder the terms:
2.5 + x = 20.353132437

Solving
2.5 + x = 20.353132437

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 = 20.353132437 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 20.353132437 + -2.5
x = 20.353132437 + -2.5

Combine like terms: 20.353132437 + -2.5 = 17.853132437
x = 17.853132437

Simplifying
x = 17.853132437


Subproblem 2
x + 2.5 = -20.353132437

Simplifying
x + 2.5 = -20.353132437

Reorder the terms:
2.5 + x = -20.353132437

Solving
2.5 + x = -20.353132437

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 = -20.353132437 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -20.353132437 + -2.5
x = -20.353132437 + -2.5

Combine like terms: -20.353132437 + -2.5 = -22.853132437
x = -22.853132437

Simplifying
x = -22.853132437


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.853132437, -22.853132437}
Solution
x = {17.853132437, -22.853132437}

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