x^2-66x+180=0

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Solution for x^2-66x+180=0 equation:


Simplifying
x2 + -66x + 180 = 0

Reorder the terms:
180 + -66x + x2 = 0

Solving
180 + -66x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-180' to each side of the equation.
180 + -66x + -180 + x2 = 0 + -180

Reorder the terms:
180 + -180 + -66x + x2 = 0 + -180

Combine like terms: 180 + -180 = 0
0 + -66x + x2 = 0 + -180
-66x + x2 = 0 + -180

Combine like terms: 0 + -180 = -180
-66x + x2 = -180

The x term is -66x.  Take half its coefficient (-33).
Square it (1089) and add it to both sides.

Add '1089' to each side of the equation.
-66x + 1089 + x2 = -180 + 1089

Reorder the terms:
1089 + -66x + x2 = -180 + 1089

Combine like terms: -180 + 1089 = 909
1089 + -66x + x2 = 909

Factor a perfect square on the left side:
(x + -33)(x + -33) = 909

Calculate the square root of the right side: 30.149626863

Break this problem into two subproblems by setting 
(x + -33) equal to 30.149626863 and -30.149626863.

Subproblem 1

x + -33 = 30.149626863 Simplifying x + -33 = 30.149626863 Reorder the terms: -33 + x = 30.149626863 Solving -33 + x = 30.149626863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '33' to each side of the equation. -33 + 33 + x = 30.149626863 + 33 Combine like terms: -33 + 33 = 0 0 + x = 30.149626863 + 33 x = 30.149626863 + 33 Combine like terms: 30.149626863 + 33 = 63.149626863 x = 63.149626863 Simplifying x = 63.149626863

Subproblem 2

x + -33 = -30.149626863 Simplifying x + -33 = -30.149626863 Reorder the terms: -33 + x = -30.149626863 Solving -33 + x = -30.149626863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '33' to each side of the equation. -33 + 33 + x = -30.149626863 + 33 Combine like terms: -33 + 33 = 0 0 + x = -30.149626863 + 33 x = -30.149626863 + 33 Combine like terms: -30.149626863 + 33 = 2.850373137 x = 2.850373137 Simplifying x = 2.850373137

Solution

The solution to the problem is based on the solutions from the subproblems. x = {63.149626863, 2.850373137}

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