x^2+12x=96

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Solution for x^2+12x=96 equation:


Simplifying
x2 + 12x = 96

Reorder the terms:
12x + x2 = 96

Solving
12x + x2 = 96

Solving for variable 'x'.

Reorder the terms:
-96 + 12x + x2 = 96 + -96

Combine like terms: 96 + -96 = 0
-96 + 12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '96' to each side of the equation.
-96 + 12x + 96 + x2 = 0 + 96

Reorder the terms:
-96 + 96 + 12x + x2 = 0 + 96

Combine like terms: -96 + 96 = 0
0 + 12x + x2 = 0 + 96
12x + x2 = 0 + 96

Combine like terms: 0 + 96 = 96
12x + x2 = 96

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 = 96 + 36

Reorder the terms:
36 + 12x + x2 = 96 + 36

Combine like terms: 96 + 36 = 132
36 + 12x + x2 = 132

Factor a perfect square on the left side:
(x + 6)(x + 6) = 132

Calculate the square root of the right side: 11.489125293

Break this problem into two subproblems by setting 
(x + 6) equal to 11.489125293 and -11.489125293.

Subproblem 1

x + 6 = 11.489125293 Simplifying x + 6 = 11.489125293 Reorder the terms: 6 + x = 11.489125293 Solving 6 + x = 11.489125293 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 = 11.489125293 + -6 Combine like terms: 6 + -6 = 0 0 + x = 11.489125293 + -6 x = 11.489125293 + -6 Combine like terms: 11.489125293 + -6 = 5.489125293 x = 5.489125293 Simplifying x = 5.489125293

Subproblem 2

x + 6 = -11.489125293 Simplifying x + 6 = -11.489125293 Reorder the terms: 6 + x = -11.489125293 Solving 6 + x = -11.489125293 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 = -11.489125293 + -6 Combine like terms: 6 + -6 = 0 0 + x = -11.489125293 + -6 x = -11.489125293 + -6 Combine like terms: -11.489125293 + -6 = -17.489125293 x = -17.489125293 Simplifying x = -17.489125293

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.489125293, -17.489125293}

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