2x^2+3x-36=0

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Solution for 2x^2+3x-36=0 equation: 


Simplifying
2x2 + 3x + -36 = 0

Reorder the terms:
-36 + 3x + 2x2 = 0

Solving
-36 + 3x + 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'.
-18 + 1.5x + x2 = 0

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + 1.5x + 18 + x2 = 0 + 18

Reorder the terms:
-18 + 18 + 1.5x + x2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + 1.5x + x2 = 0 + 18
1.5x + x2 = 0 + 18

Combine like terms: 0 + 18 = 18
1.5x + x2 = 18

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = 18 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 18 + 0.5625

Combine like terms: 18 + 0.5625 = 18.5625
0.5625 + 1.5x + x2 = 18.5625

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 18.5625

Calculate the square root of the right side: 4.308421985

Break this problem into two subproblems by setting 
(x + 0.75) equal to 4.308421985 and -4.308421985.


Subproblem 1
x + 0.75 = 4.308421985

Simplifying
x + 0.75 = 4.308421985

Reorder the terms:
0.75 + x = 4.308421985

Solving
0.75 + x = 4.308421985

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = 4.308421985 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = 4.308421985 + -0.75
x = 4.308421985 + -0.75

Combine like terms: 4.308421985 + -0.75 = 3.558421985
x = 3.558421985

Simplifying
x = 3.558421985


Subproblem 2
x + 0.75 = -4.308421985

Simplifying
x + 0.75 = -4.308421985

Reorder the terms:
0.75 + x = -4.308421985

Solving
0.75 + x = -4.308421985

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = -4.308421985 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = -4.308421985 + -0.75
x = -4.308421985 + -0.75

Combine like terms: -4.308421985 + -0.75 = -5.058421985
x = -5.058421985

Simplifying
x = -5.058421985


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.558421985, -5.058421985}

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