0=x^2-12x-15

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Solution for 0=x^2-12x-15 equation:


Simplifying
0 = x2 + -12x + -15

Reorder the terms:
0 = -15 + -12x + x2

Solving
0 = -15 + -12x + x2

Solving for variable 'x'.

Combine like terms: 0 + 15 = 15
15 + 12x + -1x2 = -15 + -12x + x2 + 15 + 12x + -1x2

Reorder the terms:
15 + 12x + -1x2 = -15 + 15 + -12x + 12x + x2 + -1x2

Combine like terms: -15 + 15 = 0
15 + 12x + -1x2 = 0 + -12x + 12x + x2 + -1x2
15 + 12x + -1x2 = -12x + 12x + x2 + -1x2

Combine like terms: -12x + 12x = 0
15 + 12x + -1x2 = 0 + x2 + -1x2
15 + 12x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
15 + 12x + -1x2 = 0

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

Divide each side by '-1'.
-15 + -12x + x2 = 0

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + -12x + 15 + x2 = 0 + 15

Reorder the terms:
-15 + 15 + -12x + x2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -12x + x2 = 0 + 15
-12x + x2 = 0 + 15

Combine like terms: 0 + 15 = 15
-12x + x2 = 15

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 = 15 + 36

Reorder the terms:
36 + -12x + x2 = 15 + 36

Combine like terms: 15 + 36 = 51
36 + -12x + x2 = 51

Factor a perfect square on the left side:
(x + -6)(x + -6) = 51

Calculate the square root of the right side: 7.141428429

Break this problem into two subproblems by setting 
(x + -6) equal to 7.141428429 and -7.141428429.

Subproblem 1

x + -6 = 7.141428429 Simplifying x + -6 = 7.141428429 Reorder the terms: -6 + x = 7.141428429 Solving -6 + x = 7.141428429 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 = 7.141428429 + 6 Combine like terms: -6 + 6 = 0 0 + x = 7.141428429 + 6 x = 7.141428429 + 6 Combine like terms: 7.141428429 + 6 = 13.141428429 x = 13.141428429 Simplifying x = 13.141428429

Subproblem 2

x + -6 = -7.141428429 Simplifying x + -6 = -7.141428429 Reorder the terms: -6 + x = -7.141428429 Solving -6 + x = -7.141428429 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 = -7.141428429 + 6 Combine like terms: -6 + 6 = 0 0 + x = -7.141428429 + 6 x = -7.141428429 + 6 Combine like terms: -7.141428429 + 6 = -1.141428429 x = -1.141428429 Simplifying x = -1.141428429

Solution

The solution to the problem is based on the solutions from the subproblems. x = {13.141428429, -1.141428429}

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