x^2-12x-256=

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Solution for x^2-12x-256= equation:


Simplifying
x2 + -12x + -256 = 0

Reorder the terms:
-256 + -12x + x2 = 0

Solving
-256 + -12x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '256' to each side of the equation.
-256 + -12x + 256 + x2 = 0 + 256

Reorder the terms:
-256 + 256 + -12x + x2 = 0 + 256

Combine like terms: -256 + 256 = 0
0 + -12x + x2 = 0 + 256
-12x + x2 = 0 + 256

Combine like terms: 0 + 256 = 256
-12x + x2 = 256

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 = 256 + 36

Reorder the terms:
36 + -12x + x2 = 256 + 36

Combine like terms: 256 + 36 = 292
36 + -12x + x2 = 292

Factor a perfect square on the left side:
(x + -6)(x + -6) = 292

Calculate the square root of the right side: 17.088007491

Break this problem into two subproblems by setting 
(x + -6) equal to 17.088007491 and -17.088007491.

Subproblem 1

x + -6 = 17.088007491 Simplifying x + -6 = 17.088007491 Reorder the terms: -6 + x = 17.088007491 Solving -6 + x = 17.088007491 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 = 17.088007491 + 6 Combine like terms: -6 + 6 = 0 0 + x = 17.088007491 + 6 x = 17.088007491 + 6 Combine like terms: 17.088007491 + 6 = 23.088007491 x = 23.088007491 Simplifying x = 23.088007491

Subproblem 2

x + -6 = -17.088007491 Simplifying x + -6 = -17.088007491 Reorder the terms: -6 + x = -17.088007491 Solving -6 + x = -17.088007491 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 = -17.088007491 + 6 Combine like terms: -6 + 6 = 0 0 + x = -17.088007491 + 6 x = -17.088007491 + 6 Combine like terms: -17.088007491 + 6 = -11.088007491 x = -11.088007491 Simplifying x = -11.088007491

Solution

The solution to the problem is based on the solutions from the subproblems. x = {23.088007491, -11.088007491}

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