(x)(x)+12x-36x+36-37=0

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Solution for (x)(x)+12x-36x+36-37=0 equation:


Simplifying
(x)(x) + 12x + -36x + 36 + -37 = 0

Multiply x * x
x2 + 12x + -36x + 36 + -37 = 0

Reorder the terms:
36 + -37 + 12x + -36x + x2 = 0

Combine like terms: 36 + -37 = -1
-1 + 12x + -36x + x2 = 0

Combine like terms: 12x + -36x = -24x
-1 + -24x + x2 = 0

Solving
-1 + -24x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -24x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -24x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -24x + x2 = 0 + 1
-24x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-24x + x2 = 1

The x term is -24x.  Take half its coefficient (-12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
-24x + 144 + x2 = 1 + 144

Reorder the terms:
144 + -24x + x2 = 1 + 144

Combine like terms: 1 + 144 = 145
144 + -24x + x2 = 145

Factor a perfect square on the left side:
(x + -12)(x + -12) = 145

Calculate the square root of the right side: 12.041594579

Break this problem into two subproblems by setting 
(x + -12) equal to 12.041594579 and -12.041594579.

Subproblem 1

x + -12 = 12.041594579 Simplifying x + -12 = 12.041594579 Reorder the terms: -12 + x = 12.041594579 Solving -12 + x = 12.041594579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 12.041594579 + 12 Combine like terms: -12 + 12 = 0 0 + x = 12.041594579 + 12 x = 12.041594579 + 12 Combine like terms: 12.041594579 + 12 = 24.041594579 x = 24.041594579 Simplifying x = 24.041594579

Subproblem 2

x + -12 = -12.041594579 Simplifying x + -12 = -12.041594579 Reorder the terms: -12 + x = -12.041594579 Solving -12 + x = -12.041594579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = -12.041594579 + 12 Combine like terms: -12 + 12 = 0 0 + x = -12.041594579 + 12 x = -12.041594579 + 12 Combine like terms: -12.041594579 + 12 = -0.041594579 x = -0.041594579 Simplifying x = -0.041594579

Solution

The solution to the problem is based on the solutions from the subproblems. x = {24.041594579, -0.041594579}

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