x^2-8x-56=0

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Solution for x^2-8x-56=0 equation:


Simplifying
x2 + -8x + -56 = 0

Reorder the terms:
-56 + -8x + x2 = 0

Solving
-56 + -8x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '56' to each side of the equation.
-56 + -8x + 56 + x2 = 0 + 56

Reorder the terms:
-56 + 56 + -8x + x2 = 0 + 56

Combine like terms: -56 + 56 = 0
0 + -8x + x2 = 0 + 56
-8x + x2 = 0 + 56

Combine like terms: 0 + 56 = 56
-8x + x2 = 56

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = 56 + 16

Reorder the terms:
16 + -8x + x2 = 56 + 16

Combine like terms: 56 + 16 = 72
16 + -8x + x2 = 72

Factor a perfect square on the left side:
(x + -4)(x + -4) = 72

Calculate the square root of the right side: 8.485281374

Break this problem into two subproblems by setting 
(x + -4) equal to 8.485281374 and -8.485281374.

Subproblem 1

x + -4 = 8.485281374 Simplifying x + -4 = 8.485281374 Reorder the terms: -4 + x = 8.485281374 Solving -4 + x = 8.485281374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 8.485281374 + 4 Combine like terms: -4 + 4 = 0 0 + x = 8.485281374 + 4 x = 8.485281374 + 4 Combine like terms: 8.485281374 + 4 = 12.485281374 x = 12.485281374 Simplifying x = 12.485281374

Subproblem 2

x + -4 = -8.485281374 Simplifying x + -4 = -8.485281374 Reorder the terms: -4 + x = -8.485281374 Solving -4 + x = -8.485281374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -8.485281374 + 4 Combine like terms: -4 + 4 = 0 0 + x = -8.485281374 + 4 x = -8.485281374 + 4 Combine like terms: -8.485281374 + 4 = -4.485281374 x = -4.485281374 Simplifying x = -4.485281374

Solution

The solution to the problem is based on the solutions from the subproblems. x = {12.485281374, -4.485281374}

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