36x+x^2=492

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Solution for 36x+x^2=492 equation:


Simplifying
36x + x2 = 492

Solving
36x + x2 = 492

Solving for variable 'x'.

Reorder the terms:
-492 + 36x + x2 = 492 + -492

Combine like terms: 492 + -492 = 0
-492 + 36x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '492' to each side of the equation.
-492 + 36x + 492 + x2 = 0 + 492

Reorder the terms:
-492 + 492 + 36x + x2 = 0 + 492

Combine like terms: -492 + 492 = 0
0 + 36x + x2 = 0 + 492
36x + x2 = 0 + 492

Combine like terms: 0 + 492 = 492
36x + x2 = 492

The x term is 36x.  Take half its coefficient (18).
Square it (324) and add it to both sides.

Add '324' to each side of the equation.
36x + 324 + x2 = 492 + 324

Reorder the terms:
324 + 36x + x2 = 492 + 324

Combine like terms: 492 + 324 = 816
324 + 36x + x2 = 816

Factor a perfect square on the left side:
(x + 18)(x + 18) = 816

Calculate the square root of the right side: 28.565713714

Break this problem into two subproblems by setting 
(x + 18) equal to 28.565713714 and -28.565713714.

Subproblem 1

x + 18 = 28.565713714 Simplifying x + 18 = 28.565713714 Reorder the terms: 18 + x = 28.565713714 Solving 18 + x = 28.565713714 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + x = 28.565713714 + -18 Combine like terms: 18 + -18 = 0 0 + x = 28.565713714 + -18 x = 28.565713714 + -18 Combine like terms: 28.565713714 + -18 = 10.565713714 x = 10.565713714 Simplifying x = 10.565713714

Subproblem 2

x + 18 = -28.565713714 Simplifying x + 18 = -28.565713714 Reorder the terms: 18 + x = -28.565713714 Solving 18 + x = -28.565713714 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + x = -28.565713714 + -18 Combine like terms: 18 + -18 = 0 0 + x = -28.565713714 + -18 x = -28.565713714 + -18 Combine like terms: -28.565713714 + -18 = -46.565713714 x = -46.565713714 Simplifying x = -46.565713714

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.565713714, -46.565713714}

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