x^2+12x-7=14

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Solution for x^2+12x-7=14 equation:


Simplifying
x2 + 12x + -7 = 14

Reorder the terms:
-7 + 12x + x2 = 14

Solving
-7 + 12x + x2 = 14

Solving for variable 'x'.

Reorder the terms:
-7 + -14 + 12x + x2 = 14 + -14

Combine like terms: -7 + -14 = -21
-21 + 12x + x2 = 14 + -14

Combine like terms: 14 + -14 = 0
-21 + 12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '21' to each side of the equation.
-21 + 12x + 21 + x2 = 0 + 21

Reorder the terms:
-21 + 21 + 12x + x2 = 0 + 21

Combine like terms: -21 + 21 = 0
0 + 12x + x2 = 0 + 21
12x + x2 = 0 + 21

Combine like terms: 0 + 21 = 21
12x + x2 = 21

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 = 21 + 36

Reorder the terms:
36 + 12x + x2 = 21 + 36

Combine like terms: 21 + 36 = 57
36 + 12x + x2 = 57

Factor a perfect square on the left side:
(x + 6)(x + 6) = 57

Calculate the square root of the right side: 7.549834435

Break this problem into two subproblems by setting 
(x + 6) equal to 7.549834435 and -7.549834435.

Subproblem 1

x + 6 = 7.549834435 Simplifying x + 6 = 7.549834435 Reorder the terms: 6 + x = 7.549834435 Solving 6 + x = 7.549834435 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 = 7.549834435 + -6 Combine like terms: 6 + -6 = 0 0 + x = 7.549834435 + -6 x = 7.549834435 + -6 Combine like terms: 7.549834435 + -6 = 1.549834435 x = 1.549834435 Simplifying x = 1.549834435

Subproblem 2

x + 6 = -7.549834435 Simplifying x + 6 = -7.549834435 Reorder the terms: 6 + x = -7.549834435 Solving 6 + x = -7.549834435 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 = -7.549834435 + -6 Combine like terms: 6 + -6 = 0 0 + x = -7.549834435 + -6 x = -7.549834435 + -6 Combine like terms: -7.549834435 + -6 = -13.549834435 x = -13.549834435 Simplifying x = -13.549834435

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.549834435, -13.549834435}

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