30=x^2-12x

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Solution for 30=x^2-12x equation:


Simplifying
30 = x2 + -12x

Reorder the terms:
30 = -12x + x2

Solving
30 = -12x + x2

Solving for variable 'x'.

Reorder the terms:
30 + 12x + -1x2 = -12x + 12x + x2 + -1x2

Combine like terms: -12x + 12x = 0
30 + 12x + -1x2 = 0 + x2 + -1x2
30 + 12x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
30 + 12x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-30 + -12x + x2 = 0

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + -12x + 30 + x2 = 0 + 30

Reorder the terms:
-30 + 30 + -12x + x2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + -12x + x2 = 0 + 30
-12x + x2 = 0 + 30

Combine like terms: 0 + 30 = 30
-12x + x2 = 30

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 = 30 + 36

Reorder the terms:
36 + -12x + x2 = 30 + 36

Combine like terms: 30 + 36 = 66
36 + -12x + x2 = 66

Factor a perfect square on the left side:
(x + -6)(x + -6) = 66

Calculate the square root of the right side: 8.124038405

Break this problem into two subproblems by setting 
(x + -6) equal to 8.124038405 and -8.124038405.

Subproblem 1

x + -6 = 8.124038405 Simplifying x + -6 = 8.124038405 Reorder the terms: -6 + x = 8.124038405 Solving -6 + x = 8.124038405 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 = 8.124038405 + 6 Combine like terms: -6 + 6 = 0 0 + x = 8.124038405 + 6 x = 8.124038405 + 6 Combine like terms: 8.124038405 + 6 = 14.124038405 x = 14.124038405 Simplifying x = 14.124038405

Subproblem 2

x + -6 = -8.124038405 Simplifying x + -6 = -8.124038405 Reorder the terms: -6 + x = -8.124038405 Solving -6 + x = -8.124038405 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 = -8.124038405 + 6 Combine like terms: -6 + 6 = 0 0 + x = -8.124038405 + 6 x = -8.124038405 + 6 Combine like terms: -8.124038405 + 6 = -2.124038405 x = -2.124038405 Simplifying x = -2.124038405

Solution

The solution to the problem is based on the solutions from the subproblems. x = {14.124038405, -2.124038405}

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