x^2-2x-42=-8

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Solution for x^2-2x-42=-8 equation: 


Simplifying
x2 + -2x + -42 = -8

Reorder the terms:
-42 + -2x + x2 = -8

Solving
-42 + -2x + x2 = -8

Solving for variable 'x'.

Reorder the terms:
-42 + 8 + -2x + x2 = -8 + 8

Combine like terms: -42 + 8 = -34
-34 + -2x + x2 = -8 + 8

Combine like terms: -8 + 8 = 0
-34 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '34' to each side of the equation.
-34 + -2x + 34 + x2 = 0 + 34

Reorder the terms:
-34 + 34 + -2x + x2 = 0 + 34

Combine like terms: -34 + 34 = 0
0 + -2x + x2 = 0 + 34
-2x + x2 = 0 + 34

Combine like terms: 0 + 34 = 34
-2x + x2 = 34

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 = 34 + 1

Reorder the terms:
1 + -2x + x2 = 34 + 1

Combine like terms: 34 + 1 = 35
1 + -2x + x2 = 35

Factor a perfect square on the left side:
(x + -1)(x + -1) = 35

Calculate the square root of the right side: 5.916079783

Break this problem into two subproblems by setting 
(x + -1) equal to 5.916079783 and -5.916079783.


Subproblem 1
x + -1 = 5.916079783

Simplifying
x + -1 = 5.916079783

Reorder the terms:
-1 + x = 5.916079783

Solving
-1 + x = 5.916079783

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 = 5.916079783 + 1

Combine like terms: -1 + 1 = 0
0 + x = 5.916079783 + 1
x = 5.916079783 + 1

Combine like terms: 5.916079783 + 1 = 6.916079783
x = 6.916079783

Simplifying
x = 6.916079783


Subproblem 2
x + -1 = -5.916079783

Simplifying
x + -1 = -5.916079783

Reorder the terms:
-1 + x = -5.916079783

Solving
-1 + x = -5.916079783

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 = -5.916079783 + 1

Combine like terms: -1 + 1 = 0
0 + x = -5.916079783 + 1
x = -5.916079783 + 1

Combine like terms: -5.916079783 + 1 = -4.916079783
x = -4.916079783

Simplifying
x = -4.916079783


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.916079783, -4.916079783}

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