x^2+12x-2988=0

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Solution for x^2+12x-2988=0 equation:


Simplifying
x2 + 12x + -2988 = 0

Reorder the terms:
-2988 + 12x + x2 = 0

Solving
-2988 + 12x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '2988' to each side of the equation.
-2988 + 12x + 2988 + x2 = 0 + 2988

Reorder the terms:
-2988 + 2988 + 12x + x2 = 0 + 2988

Combine like terms: -2988 + 2988 = 0
0 + 12x + x2 = 0 + 2988
12x + x2 = 0 + 2988

Combine like terms: 0 + 2988 = 2988
12x + x2 = 2988

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 = 2988 + 36

Reorder the terms:
36 + 12x + x2 = 2988 + 36

Combine like terms: 2988 + 36 = 3024
36 + 12x + x2 = 3024

Factor a perfect square on the left side:
(x + 6)(x + 6) = 3024

Calculate the square root of the right side: 54.990908339

Break this problem into two subproblems by setting 
(x + 6) equal to 54.990908339 and -54.990908339.

Subproblem 1

x + 6 = 54.990908339 Simplifying x + 6 = 54.990908339 Reorder the terms: 6 + x = 54.990908339 Solving 6 + x = 54.990908339 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 = 54.990908339 + -6 Combine like terms: 6 + -6 = 0 0 + x = 54.990908339 + -6 x = 54.990908339 + -6 Combine like terms: 54.990908339 + -6 = 48.990908339 x = 48.990908339 Simplifying x = 48.990908339

Subproblem 2

x + 6 = -54.990908339 Simplifying x + 6 = -54.990908339 Reorder the terms: 6 + x = -54.990908339 Solving 6 + x = -54.990908339 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 = -54.990908339 + -6 Combine like terms: 6 + -6 = 0 0 + x = -54.990908339 + -6 x = -54.990908339 + -6 Combine like terms: -54.990908339 + -6 = -60.990908339 x = -60.990908339 Simplifying x = -60.990908339

Solution

The solution to the problem is based on the solutions from the subproblems. x = {48.990908339, -60.990908339}

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