-.05x^2+36x-126=396

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Solution for -.05x^2+36x-126=396 equation: 


Simplifying
-0.05x2 + 36x + -126 = 396

Reorder the terms:
-126 + 36x + -0.05x2 = 396

Solving
-126 + 36x + -0.05x2 = 396

Solving for variable 'x'.

Reorder the terms:
-126 + -396 + 36x + -0.05x2 = 396 + -396

Combine like terms: -126 + -396 = -522
-522 + 36x + -0.05x2 = 396 + -396

Combine like terms: 396 + -396 = 0
-522 + 36x + -0.05x2 = 0

Begin completing the square.  Divide all terms by
-0.05 the coefficient of the squared term: 

Divide each side by '-0.05'.
10440 + -720x + x2 = 0

Move the constant term to the right:

Add '-10440' to each side of the equation.
10440 + -720x + -10440 + x2 = 0 + -10440

Reorder the terms:
10440 + -10440 + -720x + x2 = 0 + -10440

Combine like terms: 10440 + -10440 = 0
0 + -720x + x2 = 0 + -10440
-720x + x2 = 0 + -10440

Combine like terms: 0 + -10440 = -10440
-720x + x2 = -10440

The x term is -720x.  Take half its coefficient (-360).
Square it (129600) and add it to both sides.

Add '129600' to each side of the equation.
-720x + 129600 + x2 = -10440 + 129600

Reorder the terms:
129600 + -720x + x2 = -10440 + 129600

Combine like terms: -10440 + 129600 = 119160
129600 + -720x + x2 = 119160

Factor a perfect square on the left side:
(x + -360)(x + -360) = 119160

Calculate the square root of the right side: 345.195596727

Break this problem into two subproblems by setting 
(x + -360) equal to 345.195596727 and -345.195596727.


Subproblem 1
x + -360 = 345.195596727

Simplifying
x + -360 = 345.195596727

Reorder the terms:
-360 + x = 345.195596727

Solving
-360 + x = 345.195596727

Solving for variable 'x'.

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

Add '360' to each side of the equation.
-360 + 360 + x = 345.195596727 + 360

Combine like terms: -360 + 360 = 0
0 + x = 345.195596727 + 360
x = 345.195596727 + 360

Combine like terms: 345.195596727 + 360 = 705.195596727
x = 705.195596727

Simplifying
x = 705.195596727


Subproblem 2
x + -360 = -345.195596727

Simplifying
x + -360 = -345.195596727

Reorder the terms:
-360 + x = -345.195596727

Solving
-360 + x = -345.195596727

Solving for variable 'x'.

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

Add '360' to each side of the equation.
-360 + 360 + x = -345.195596727 + 360

Combine like terms: -360 + 360 = 0
0 + x = -345.195596727 + 360
x = -345.195596727 + 360

Combine like terms: -345.195596727 + 360 = 14.804403273
x = 14.804403273

Simplifying
x = 14.804403273


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {705.195596727, 14.804403273}

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