0=x^2-12x-300

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Solution for 0=x^2-12x-300 equation:


Simplifying
0 = x2 + -12x + -300

Reorder the terms:
0 = -300 + -12x + x2

Solving
0 = -300 + -12x + x2

Solving for variable 'x'.

Combine like terms: 0 + 300 = 300
300 + 12x + -1x2 = -300 + -12x + x2 + 300 + 12x + -1x2

Reorder the terms:
300 + 12x + -1x2 = -300 + 300 + -12x + 12x + x2 + -1x2

Combine like terms: -300 + 300 = 0
300 + 12x + -1x2 = 0 + -12x + 12x + x2 + -1x2
300 + 12x + -1x2 = -12x + 12x + x2 + -1x2

Combine like terms: -12x + 12x = 0
300 + 12x + -1x2 = 0 + x2 + -1x2
300 + 12x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
300 + 12x + -1x2 = 0

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

Divide each side by '-1'.
-300 + -12x + x2 = 0

Move the constant term to the right:

Add '300' to each side of the equation.
-300 + -12x + 300 + x2 = 0 + 300

Reorder the terms:
-300 + 300 + -12x + x2 = 0 + 300

Combine like terms: -300 + 300 = 0
0 + -12x + x2 = 0 + 300
-12x + x2 = 0 + 300

Combine like terms: 0 + 300 = 300
-12x + x2 = 300

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 = 300 + 36

Reorder the terms:
36 + -12x + x2 = 300 + 36

Combine like terms: 300 + 36 = 336
36 + -12x + x2 = 336

Factor a perfect square on the left side:
(x + -6)(x + -6) = 336

Calculate the square root of the right side: 18.33030278

Break this problem into two subproblems by setting 
(x + -6) equal to 18.33030278 and -18.33030278.

Subproblem 1

x + -6 = 18.33030278 Simplifying x + -6 = 18.33030278 Reorder the terms: -6 + x = 18.33030278 Solving -6 + x = 18.33030278 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 = 18.33030278 + 6 Combine like terms: -6 + 6 = 0 0 + x = 18.33030278 + 6 x = 18.33030278 + 6 Combine like terms: 18.33030278 + 6 = 24.33030278 x = 24.33030278 Simplifying x = 24.33030278

Subproblem 2

x + -6 = -18.33030278 Simplifying x + -6 = -18.33030278 Reorder the terms: -6 + x = -18.33030278 Solving -6 + x = -18.33030278 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 = -18.33030278 + 6 Combine like terms: -6 + 6 = 0 0 + x = -18.33030278 + 6 x = -18.33030278 + 6 Combine like terms: -18.33030278 + 6 = -12.33030278 x = -12.33030278 Simplifying x = -12.33030278

Solution

The solution to the problem is based on the solutions from the subproblems. x = {24.33030278, -12.33030278}

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