2x^2-18x-364=0

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Solution for 2x^2-18x-364=0 equation: 


Simplifying
2x2 + -18x + -364 = 0

Reorder the terms:
-364 + -18x + 2x2 = 0

Solving
-364 + -18x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-182 + -9x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-182 + -9x + x2)' equal to zero and attempt to solve:

Simplifying
-182 + -9x + x2 = 0

Solving
-182 + -9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '182' to each side of the equation.
-182 + -9x + 182 + x2 = 0 + 182

Reorder the terms:
-182 + 182 + -9x + x2 = 0 + 182

Combine like terms: -182 + 182 = 0
0 + -9x + x2 = 0 + 182
-9x + x2 = 0 + 182

Combine like terms: 0 + 182 = 182
-9x + x2 = 182

The x term is -9x.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9x + 20.25 + x2 = 182 + 20.25

Reorder the terms:
20.25 + -9x + x2 = 182 + 20.25

Combine like terms: 182 + 20.25 = 202.25
20.25 + -9x + x2 = 202.25

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 202.25

Calculate the square root of the right side: 14.221462653

Break this problem into two subproblems by setting 
(x + -4.5) equal to 14.221462653 and -14.221462653.


Subproblem 1
x + -4.5 = 14.221462653

Simplifying
x + -4.5 = 14.221462653

Reorder the terms:
-4.5 + x = 14.221462653

Solving
-4.5 + x = 14.221462653

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = 14.221462653 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = 14.221462653 + 4.5
x = 14.221462653 + 4.5

Combine like terms: 14.221462653 + 4.5 = 18.721462653
x = 18.721462653

Simplifying
x = 18.721462653


Subproblem 2
x + -4.5 = -14.221462653

Simplifying
x + -4.5 = -14.221462653

Reorder the terms:
-4.5 + x = -14.221462653

Solving
-4.5 + x = -14.221462653

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = -14.221462653 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = -14.221462653 + 4.5
x = -14.221462653 + 4.5

Combine like terms: -14.221462653 + 4.5 = -9.721462653
x = -9.721462653

Simplifying
x = -9.721462653


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {18.721462653, -9.721462653}
Solution
x = {18.721462653, -9.721462653}

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