x^2+12x-48=0

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Solution for x^2+12x-48=0 equation:


Simplifying
x2 + 12x + -48 = 0

Reorder the terms:
-48 + 12x + x2 = 0

Solving
-48 + 12x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '48' to each side of the equation.
-48 + 12x + 48 + x2 = 0 + 48

Reorder the terms:
-48 + 48 + 12x + x2 = 0 + 48

Combine like terms: -48 + 48 = 0
0 + 12x + x2 = 0 + 48
12x + x2 = 0 + 48

Combine like terms: 0 + 48 = 48
12x + x2 = 48

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 = 48 + 36

Reorder the terms:
36 + 12x + x2 = 48 + 36

Combine like terms: 48 + 36 = 84
36 + 12x + x2 = 84

Factor a perfect square on the left side:
(x + 6)(x + 6) = 84

Calculate the square root of the right side: 9.16515139

Break this problem into two subproblems by setting 
(x + 6) equal to 9.16515139 and -9.16515139.

Subproblem 1

x + 6 = 9.16515139 Simplifying x + 6 = 9.16515139 Reorder the terms: 6 + x = 9.16515139 Solving 6 + x = 9.16515139 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 = 9.16515139 + -6 Combine like terms: 6 + -6 = 0 0 + x = 9.16515139 + -6 x = 9.16515139 + -6 Combine like terms: 9.16515139 + -6 = 3.16515139 x = 3.16515139 Simplifying x = 3.16515139

Subproblem 2

x + 6 = -9.16515139 Simplifying x + 6 = -9.16515139 Reorder the terms: 6 + x = -9.16515139 Solving 6 + x = -9.16515139 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 = -9.16515139 + -6 Combine like terms: 6 + -6 = 0 0 + x = -9.16515139 + -6 x = -9.16515139 + -6 Combine like terms: -9.16515139 + -6 = -15.16515139 x = -15.16515139 Simplifying x = -15.16515139

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.16515139, -15.16515139}

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