x^2+12x-27=0

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Solution for x^2+12x-27=0 equation:


Simplifying
x2 + 12x + -27 = 0

Reorder the terms:
-27 + 12x + x2 = 0

Solving
-27 + 12x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '27' to each side of the equation.
-27 + 12x + 27 + x2 = 0 + 27

Reorder the terms:
-27 + 27 + 12x + x2 = 0 + 27

Combine like terms: -27 + 27 = 0
0 + 12x + x2 = 0 + 27
12x + x2 = 0 + 27

Combine like terms: 0 + 27 = 27
12x + x2 = 27

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 = 27 + 36

Reorder the terms:
36 + 12x + x2 = 27 + 36

Combine like terms: 27 + 36 = 63
36 + 12x + x2 = 63

Factor a perfect square on the left side:
(x + 6)(x + 6) = 63

Calculate the square root of the right side: 7.937253933

Break this problem into two subproblems by setting 
(x + 6) equal to 7.937253933 and -7.937253933.

Subproblem 1

x + 6 = 7.937253933 Simplifying x + 6 = 7.937253933 Reorder the terms: 6 + x = 7.937253933 Solving 6 + x = 7.937253933 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 = 7.937253933 + -6 Combine like terms: 6 + -6 = 0 0 + x = 7.937253933 + -6 x = 7.937253933 + -6 Combine like terms: 7.937253933 + -6 = 1.937253933 x = 1.937253933 Simplifying x = 1.937253933

Subproblem 2

x + 6 = -7.937253933 Simplifying x + 6 = -7.937253933 Reorder the terms: 6 + x = -7.937253933 Solving 6 + x = -7.937253933 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 = -7.937253933 + -6 Combine like terms: 6 + -6 = 0 0 + x = -7.937253933 + -6 x = -7.937253933 + -6 Combine like terms: -7.937253933 + -6 = -13.937253933 x = -13.937253933 Simplifying x = -13.937253933

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.937253933, -13.937253933}

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