x(x-12)=60

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Solution for x(x-12)=60 equation:


Simplifying
x(x + -12) = 60

Reorder the terms:
x(-12 + x) = 60
(-12 * x + x * x) = 60
(-12x + x2) = 60

Solving
-12x + x2 = 60

Solving for variable 'x'.

Reorder the terms:
-60 + -12x + x2 = 60 + -60

Combine like terms: 60 + -60 = 0
-60 + -12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '60' to each side of the equation.
-60 + -12x + 60 + x2 = 0 + 60

Reorder the terms:
-60 + 60 + -12x + x2 = 0 + 60

Combine like terms: -60 + 60 = 0
0 + -12x + x2 = 0 + 60
-12x + x2 = 0 + 60

Combine like terms: 0 + 60 = 60
-12x + x2 = 60

The x term is -12x.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12x + 36 + x2 = 60 + 36

Reorder the terms:
36 + -12x + x2 = 60 + 36

Combine like terms: 60 + 36 = 96
36 + -12x + x2 = 96

Factor a perfect square on the left side:
(x + -6)(x + -6) = 96

Calculate the square root of the right side: 9.797958971

Break this problem into two subproblems by setting 
(x + -6) equal to 9.797958971 and -9.797958971.

Subproblem 1

x + -6 = 9.797958971 Simplifying x + -6 = 9.797958971 Reorder the terms: -6 + x = 9.797958971 Solving -6 + x = 9.797958971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 9.797958971 + 6 Combine like terms: -6 + 6 = 0 0 + x = 9.797958971 + 6 x = 9.797958971 + 6 Combine like terms: 9.797958971 + 6 = 15.797958971 x = 15.797958971 Simplifying x = 15.797958971

Subproblem 2

x + -6 = -9.797958971 Simplifying x + -6 = -9.797958971 Reorder the terms: -6 + x = -9.797958971 Solving -6 + x = -9.797958971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -9.797958971 + 6 Combine like terms: -6 + 6 = 0 0 + x = -9.797958971 + 6 x = -9.797958971 + 6 Combine like terms: -9.797958971 + 6 = -3.797958971 x = -3.797958971 Simplifying x = -3.797958971

Solution

The solution to the problem is based on the solutions from the subproblems. x = {15.797958971, -3.797958971}

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