x^2-60x-648=0

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Solution for x^2-60x-648=0 equation:


Simplifying
x2 + -60x + -648 = 0

Reorder the terms:
-648 + -60x + x2 = 0

Solving
-648 + -60x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '648' to each side of the equation.
-648 + -60x + 648 + x2 = 0 + 648

Reorder the terms:
-648 + 648 + -60x + x2 = 0 + 648

Combine like terms: -648 + 648 = 0
0 + -60x + x2 = 0 + 648
-60x + x2 = 0 + 648

Combine like terms: 0 + 648 = 648
-60x + x2 = 648

The x term is -60x.  Take half its coefficient (-30).
Square it (900) and add it to both sides.

Add '900' to each side of the equation.
-60x + 900 + x2 = 648 + 900

Reorder the terms:
900 + -60x + x2 = 648 + 900

Combine like terms: 648 + 900 = 1548
900 + -60x + x2 = 1548

Factor a perfect square on the left side:
(x + -30)(x + -30) = 1548

Calculate the square root of the right side: 39.344631146

Break this problem into two subproblems by setting 
(x + -30) equal to 39.344631146 and -39.344631146.

Subproblem 1

x + -30 = 39.344631146 Simplifying x + -30 = 39.344631146 Reorder the terms: -30 + x = 39.344631146 Solving -30 + x = 39.344631146 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = 39.344631146 + 30 Combine like terms: -30 + 30 = 0 0 + x = 39.344631146 + 30 x = 39.344631146 + 30 Combine like terms: 39.344631146 + 30 = 69.344631146 x = 69.344631146 Simplifying x = 69.344631146

Subproblem 2

x + -30 = -39.344631146 Simplifying x + -30 = -39.344631146 Reorder the terms: -30 + x = -39.344631146 Solving -30 + x = -39.344631146 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = -39.344631146 + 30 Combine like terms: -30 + 30 = 0 0 + x = -39.344631146 + 30 x = -39.344631146 + 30 Combine like terms: -39.344631146 + 30 = -9.344631146 x = -9.344631146 Simplifying x = -9.344631146

Solution

The solution to the problem is based on the solutions from the subproblems. x = {69.344631146, -9.344631146}

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