0=x^2+16x-96

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Solution for 0=x^2+16x-96 equation:


Simplifying
0 = x2 + 16x + -96

Reorder the terms:
0 = -96 + 16x + x2

Solving
0 = -96 + 16x + x2

Solving for variable 'x'.

Combine like terms: 0 + 96 = 96
96 + -16x + -1x2 = -96 + 16x + x2 + 96 + -16x + -1x2

Reorder the terms:
96 + -16x + -1x2 = -96 + 96 + 16x + -16x + x2 + -1x2

Combine like terms: -96 + 96 = 0
96 + -16x + -1x2 = 0 + 16x + -16x + x2 + -1x2
96 + -16x + -1x2 = 16x + -16x + x2 + -1x2

Combine like terms: 16x + -16x = 0
96 + -16x + -1x2 = 0 + x2 + -1x2
96 + -16x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
96 + -16x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-96 + 16x + x2 = 0

Move the constant term to the right:

Add '96' to each side of the equation.
-96 + 16x + 96 + x2 = 0 + 96

Reorder the terms:
-96 + 96 + 16x + x2 = 0 + 96

Combine like terms: -96 + 96 = 0
0 + 16x + x2 = 0 + 96
16x + x2 = 0 + 96

Combine like terms: 0 + 96 = 96
16x + x2 = 96

The x term is 16x.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16x + 64 + x2 = 96 + 64

Reorder the terms:
64 + 16x + x2 = 96 + 64

Combine like terms: 96 + 64 = 160
64 + 16x + x2 = 160

Factor a perfect square on the left side:
(x + 8)(x + 8) = 160

Calculate the square root of the right side: 12.649110641

Break this problem into two subproblems by setting 
(x + 8) equal to 12.649110641 and -12.649110641.

Subproblem 1

x + 8 = 12.649110641 Simplifying x + 8 = 12.649110641 Reorder the terms: 8 + x = 12.649110641 Solving 8 + x = 12.649110641 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 12.649110641 + -8 Combine like terms: 8 + -8 = 0 0 + x = 12.649110641 + -8 x = 12.649110641 + -8 Combine like terms: 12.649110641 + -8 = 4.649110641 x = 4.649110641 Simplifying x = 4.649110641

Subproblem 2

x + 8 = -12.649110641 Simplifying x + 8 = -12.649110641 Reorder the terms: 8 + x = -12.649110641 Solving 8 + x = -12.649110641 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -12.649110641 + -8 Combine like terms: 8 + -8 = 0 0 + x = -12.649110641 + -8 x = -12.649110641 + -8 Combine like terms: -12.649110641 + -8 = -20.649110641 x = -20.649110641 Simplifying x = -20.649110641

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.649110641, -20.649110641}

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