x^2-32x-128=0

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Solution for x^2-32x-128=0 equation:


Simplifying
x2 + -32x + -128 = 0

Reorder the terms:
-128 + -32x + x2 = 0

Solving
-128 + -32x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '128' to each side of the equation.
-128 + -32x + 128 + x2 = 0 + 128

Reorder the terms:
-128 + 128 + -32x + x2 = 0 + 128

Combine like terms: -128 + 128 = 0
0 + -32x + x2 = 0 + 128
-32x + x2 = 0 + 128

Combine like terms: 0 + 128 = 128
-32x + x2 = 128

The x term is -32x.  Take half its coefficient (-16).
Square it (256) and add it to both sides.

Add '256' to each side of the equation.
-32x + 256 + x2 = 128 + 256

Reorder the terms:
256 + -32x + x2 = 128 + 256

Combine like terms: 128 + 256 = 384
256 + -32x + x2 = 384

Factor a perfect square on the left side:
(x + -16)(x + -16) = 384

Calculate the square root of the right side: 19.595917942

Break this problem into two subproblems by setting 
(x + -16) equal to 19.595917942 and -19.595917942.

Subproblem 1

x + -16 = 19.595917942 Simplifying x + -16 = 19.595917942 Reorder the terms: -16 + x = 19.595917942 Solving -16 + x = 19.595917942 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = 19.595917942 + 16 Combine like terms: -16 + 16 = 0 0 + x = 19.595917942 + 16 x = 19.595917942 + 16 Combine like terms: 19.595917942 + 16 = 35.595917942 x = 35.595917942 Simplifying x = 35.595917942

Subproblem 2

x + -16 = -19.595917942 Simplifying x + -16 = -19.595917942 Reorder the terms: -16 + x = -19.595917942 Solving -16 + x = -19.595917942 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = -19.595917942 + 16 Combine like terms: -16 + 16 = 0 0 + x = -19.595917942 + 16 x = -19.595917942 + 16 Combine like terms: -19.595917942 + 16 = -3.595917942 x = -3.595917942 Simplifying x = -3.595917942

Solution

The solution to the problem is based on the solutions from the subproblems. x = {35.595917942, -3.595917942}

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