2x^2+7x-36=0

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Solution for 2x^2+7x-36=0 equation: 


Simplifying
2x2 + 7x + -36 = 0

Reorder the terms:
-36 + 7x + 2x2 = 0

Solving
-36 + 7x + 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 + 3.5x + x2 = 0

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + 3.5x + 18 + x2 = 0 + 18

Reorder the terms:
-18 + 18 + 3.5x + x2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + 3.5x + x2 = 0 + 18
3.5x + x2 = 0 + 18

Combine like terms: 0 + 18 = 18
3.5x + x2 = 18

The x term is 3.5x.  Take half its coefficient (1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
3.5x + 3.0625 + x2 = 18 + 3.0625

Reorder the terms:
3.0625 + 3.5x + x2 = 18 + 3.0625

Combine like terms: 18 + 3.0625 = 21.0625
3.0625 + 3.5x + x2 = 21.0625

Factor a perfect square on the left side:
(x + 1.75)(x + 1.75) = 21.0625

Calculate the square root of the right side: 4.589389938

Break this problem into two subproblems by setting 
(x + 1.75) equal to 4.589389938 and -4.589389938.


Subproblem 1
x + 1.75 = 4.589389938

Simplifying
x + 1.75 = 4.589389938

Reorder the terms:
1.75 + x = 4.589389938

Solving
1.75 + x = 4.589389938

Solving for variable 'x'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + x = 4.589389938 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = 4.589389938 + -1.75
x = 4.589389938 + -1.75

Combine like terms: 4.589389938 + -1.75 = 2.839389938
x = 2.839389938

Simplifying
x = 2.839389938


Subproblem 2
x + 1.75 = -4.589389938

Simplifying
x + 1.75 = -4.589389938

Reorder the terms:
1.75 + x = -4.589389938

Solving
1.75 + x = -4.589389938

Solving for variable 'x'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + x = -4.589389938 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = -4.589389938 + -1.75
x = -4.589389938 + -1.75

Combine like terms: -4.589389938 + -1.75 = -6.339389938
x = -6.339389938

Simplifying
x = -6.339389938


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.839389938, -6.339389938}

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