594=0.5x^2+36x

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Solution for 594=0.5x^2+36x equation: 


Simplifying
594 = 0.5x2 + 36x

Reorder the terms:
594 = 36x + 0.5x2

Solving
594 = 36x + 0.5x2

Solving for variable 'x'.

Reorder the terms:
594 + -36x + -0.5x2 = 36x + -36x + 0.5x2 + -0.5x2

Combine like terms: 36x + -36x = 0
594 + -36x + -0.5x2 = 0 + 0.5x2 + -0.5x2
594 + -36x + -0.5x2 = 0.5x2 + -0.5x2

Combine like terms: 0.5x2 + -0.5x2 = 0.0
594 + -36x + -0.5x2 = 0.0

Begin completing the square.  Divide all terms by
-0.5 the coefficient of the squared term: 

Divide each side by '-0.5'.
-1188 + 72x + x2 = 0

Move the constant term to the right:

Add '1188' to each side of the equation.
-1188 + 72x + 1188 + x2 = 0 + 1188

Reorder the terms:
-1188 + 1188 + 72x + x2 = 0 + 1188

Combine like terms: -1188 + 1188 = 0
0 + 72x + x2 = 0 + 1188
72x + x2 = 0 + 1188

Combine like terms: 0 + 1188 = 1188
72x + x2 = 1188

The x term is 72x.  Take half its coefficient (36).
Square it (1296) and add it to both sides.

Add '1296' to each side of the equation.
72x + 1296 + x2 = 1188 + 1296

Reorder the terms:
1296 + 72x + x2 = 1188 + 1296

Combine like terms: 1188 + 1296 = 2484
1296 + 72x + x2 = 2484

Factor a perfect square on the left side:
(x + 36)(x + 36) = 2484

Calculate the square root of the right side: 49.839743178

Break this problem into two subproblems by setting 
(x + 36) equal to 49.839743178 and -49.839743178.


Subproblem 1
x + 36 = 49.839743178

Simplifying
x + 36 = 49.839743178

Reorder the terms:
36 + x = 49.839743178

Solving
36 + x = 49.839743178

Solving for variable 'x'.

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

Add '-36' to each side of the equation.
36 + -36 + x = 49.839743178 + -36

Combine like terms: 36 + -36 = 0
0 + x = 49.839743178 + -36
x = 49.839743178 + -36

Combine like terms: 49.839743178 + -36 = 13.839743178
x = 13.839743178

Simplifying
x = 13.839743178


Subproblem 2
x + 36 = -49.839743178

Simplifying
x + 36 = -49.839743178

Reorder the terms:
36 + x = -49.839743178

Solving
36 + x = -49.839743178

Solving for variable 'x'.

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

Add '-36' to each side of the equation.
36 + -36 + x = -49.839743178 + -36

Combine like terms: 36 + -36 = 0
0 + x = -49.839743178 + -36
x = -49.839743178 + -36

Combine like terms: -49.839743178 + -36 = -85.839743178
x = -85.839743178

Simplifying
x = -85.839743178


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.839743178, -85.839743178}

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