x^2-2x-56=6

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Solution for x^2-2x-56=6 equation:


Simplifying
x2 + -2x + -56 = 6

Reorder the terms:
-56 + -2x + x2 = 6

Solving
-56 + -2x + x2 = 6

Solving for variable 'x'.

Reorder the terms:
-56 + -6 + -2x + x2 = 6 + -6

Combine like terms: -56 + -6 = -62
-62 + -2x + x2 = 6 + -6

Combine like terms: 6 + -6 = 0
-62 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '62' to each side of the equation.
-62 + -2x + 62 + x2 = 0 + 62

Reorder the terms:
-62 + 62 + -2x + x2 = 0 + 62

Combine like terms: -62 + 62 = 0
0 + -2x + x2 = 0 + 62
-2x + x2 = 0 + 62

Combine like terms: 0 + 62 = 62
-2x + x2 = 62

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 62 + 1

Reorder the terms:
1 + -2x + x2 = 62 + 1

Combine like terms: 62 + 1 = 63
1 + -2x + x2 = 63

Factor a perfect square on the left side:
(x + -1)(x + -1) = 63

Calculate the square root of the right side: 7.937253933

Break this problem into two subproblems by setting 
(x + -1) equal to 7.937253933 and -7.937253933.

Subproblem 1

x + -1 = 7.937253933 Simplifying x + -1 = 7.937253933 Reorder the terms: -1 + x = 7.937253933 Solving -1 + x = 7.937253933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 7.937253933 + 1 Combine like terms: -1 + 1 = 0 0 + x = 7.937253933 + 1 x = 7.937253933 + 1 Combine like terms: 7.937253933 + 1 = 8.937253933 x = 8.937253933 Simplifying x = 8.937253933

Subproblem 2

x + -1 = -7.937253933 Simplifying x + -1 = -7.937253933 Reorder the terms: -1 + x = -7.937253933 Solving -1 + x = -7.937253933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -7.937253933 + 1 Combine like terms: -1 + 1 = 0 0 + x = -7.937253933 + 1 x = -7.937253933 + 1 Combine like terms: -7.937253933 + 1 = -6.937253933 x = -6.937253933 Simplifying x = -6.937253933

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.937253933, -6.937253933}

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