x^2-16x-144=0

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Solution for x^2-16x-144=0 equation:


Simplifying
x2 + -16x + -144 = 0

Reorder the terms:
-144 + -16x + x2 = 0

Solving
-144 + -16x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '144' to each side of the equation.
-144 + -16x + 144 + x2 = 0 + 144

Reorder the terms:
-144 + 144 + -16x + x2 = 0 + 144

Combine like terms: -144 + 144 = 0
0 + -16x + x2 = 0 + 144
-16x + x2 = 0 + 144

Combine like terms: 0 + 144 = 144
-16x + x2 = 144

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 = 144 + 64

Reorder the terms:
64 + -16x + x2 = 144 + 64

Combine like terms: 144 + 64 = 208
64 + -16x + x2 = 208

Factor a perfect square on the left side:
(x + -8)(x + -8) = 208

Calculate the square root of the right side: 14.422205102

Break this problem into two subproblems by setting 
(x + -8) equal to 14.422205102 and -14.422205102.

Subproblem 1

x + -8 = 14.422205102 Simplifying x + -8 = 14.422205102 Reorder the terms: -8 + x = 14.422205102 Solving -8 + x = 14.422205102 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 = 14.422205102 + 8 Combine like terms: -8 + 8 = 0 0 + x = 14.422205102 + 8 x = 14.422205102 + 8 Combine like terms: 14.422205102 + 8 = 22.422205102 x = 22.422205102 Simplifying x = 22.422205102

Subproblem 2

x + -8 = -14.422205102 Simplifying x + -8 = -14.422205102 Reorder the terms: -8 + x = -14.422205102 Solving -8 + x = -14.422205102 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 = -14.422205102 + 8 Combine like terms: -8 + 8 = 0 0 + x = -14.422205102 + 8 x = -14.422205102 + 8 Combine like terms: -14.422205102 + 8 = -6.422205102 x = -6.422205102 Simplifying x = -6.422205102

Solution

The solution to the problem is based on the solutions from the subproblems. x = {22.422205102, -6.422205102}

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