2x^2+9x-136=0

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Solution for 2x^2+9x-136=0 equation: 


Simplifying
2x2 + 9x + -136 = 0

Reorder the terms:
-136 + 9x + 2x2 = 0

Solving
-136 + 9x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
-68 + 4.5x + x2 = 0

Move the constant term to the right:

Add '68' to each side of the equation.
-68 + 4.5x + 68 + x2 = 0 + 68

Reorder the terms:
-68 + 68 + 4.5x + x2 = 0 + 68

Combine like terms: -68 + 68 = 0
0 + 4.5x + x2 = 0 + 68
4.5x + x2 = 0 + 68

Combine like terms: 0 + 68 = 68
4.5x + x2 = 68

The x term is 4.5x.  Take half its coefficient (2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
4.5x + 5.0625 + x2 = 68 + 5.0625

Reorder the terms:
5.0625 + 4.5x + x2 = 68 + 5.0625

Combine like terms: 68 + 5.0625 = 73.0625
5.0625 + 4.5x + x2 = 73.0625

Factor a perfect square on the left side:
(x + 2.25)(x + 2.25) = 73.0625

Calculate the square root of the right side: 8.547660499

Break this problem into two subproblems by setting 
(x + 2.25) equal to 8.547660499 and -8.547660499.


Subproblem 1
x + 2.25 = 8.547660499

Simplifying
x + 2.25 = 8.547660499

Reorder the terms:
2.25 + x = 8.547660499

Solving
2.25 + x = 8.547660499

Solving for variable 'x'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + x = 8.547660499 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + x = 8.547660499 + -2.25
x = 8.547660499 + -2.25

Combine like terms: 8.547660499 + -2.25 = 6.297660499
x = 6.297660499

Simplifying
x = 6.297660499


Subproblem 2
x + 2.25 = -8.547660499

Simplifying
x + 2.25 = -8.547660499

Reorder the terms:
2.25 + x = -8.547660499

Solving
2.25 + x = -8.547660499

Solving for variable 'x'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + x = -8.547660499 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + x = -8.547660499 + -2.25
x = -8.547660499 + -2.25

Combine like terms: -8.547660499 + -2.25 = -10.797660499
x = -10.797660499

Simplifying
x = -10.797660499


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.297660499, -10.797660499}

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