(x*x)+12x-24=0

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Solution for (x*x)+12x-24=0 equation:


Simplifying
(x * x) + 12x + -24 = 0

Multiply x * x
(x2) + 12x + -24 = 0
x2 + 12x + -24 = 0

Reorder the terms:
-24 + 12x + x2 = 0

Solving
-24 + 12x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + 12x + 24 + x2 = 0 + 24

Reorder the terms:
-24 + 24 + 12x + x2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + 12x + x2 = 0 + 24
12x + x2 = 0 + 24

Combine like terms: 0 + 24 = 24
12x + x2 = 24

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 = 24 + 36

Reorder the terms:
36 + 12x + x2 = 24 + 36

Combine like terms: 24 + 36 = 60
36 + 12x + x2 = 60

Factor a perfect square on the left side:
(x + 6)(x + 6) = 60

Calculate the square root of the right side: 7.745966692

Break this problem into two subproblems by setting 
(x + 6) equal to 7.745966692 and -7.745966692.

Subproblem 1

x + 6 = 7.745966692 Simplifying x + 6 = 7.745966692 Reorder the terms: 6 + x = 7.745966692 Solving 6 + x = 7.745966692 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 = 7.745966692 + -6 Combine like terms: 6 + -6 = 0 0 + x = 7.745966692 + -6 x = 7.745966692 + -6 Combine like terms: 7.745966692 + -6 = 1.745966692 x = 1.745966692 Simplifying x = 1.745966692

Subproblem 2

x + 6 = -7.745966692 Simplifying x + 6 = -7.745966692 Reorder the terms: 6 + x = -7.745966692 Solving 6 + x = -7.745966692 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 = -7.745966692 + -6 Combine like terms: 6 + -6 = 0 0 + x = -7.745966692 + -6 x = -7.745966692 + -6 Combine like terms: -7.745966692 + -6 = -13.745966692 x = -13.745966692 Simplifying x = -13.745966692

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.745966692, -13.745966692}

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