x^2-1x-42=42

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Solution for x^2-1x-42=42 equation:


Simplifying
x2 + -1x + -42 = 42

Reorder the terms:
-42 + -1x + x2 = 42

Solving
-42 + -1x + x2 = 42

Solving for variable 'x'.

Reorder the terms:
-42 + -42 + -1x + x2 = 42 + -42

Combine like terms: -42 + -42 = -84
-84 + -1x + x2 = 42 + -42

Combine like terms: 42 + -42 = 0
-84 + -1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '84' to each side of the equation.
-84 + -1x + 84 + x2 = 0 + 84

Reorder the terms:
-84 + 84 + -1x + x2 = 0 + 84

Combine like terms: -84 + 84 = 0
0 + -1x + x2 = 0 + 84
-1x + x2 = 0 + 84

Combine like terms: 0 + 84 = 84
-1x + x2 = 84

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 84 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 84 + 0.25

Combine like terms: 84 + 0.25 = 84.25
0.25 + -1x + x2 = 84.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 84.25

Calculate the square root of the right side: 9.178779875

Break this problem into two subproblems by setting 
(x + -0.5) equal to 9.178779875 and -9.178779875.

Subproblem 1

x + -0.5 = 9.178779875 Simplifying x + -0.5 = 9.178779875 Reorder the terms: -0.5 + x = 9.178779875 Solving -0.5 + x = 9.178779875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 9.178779875 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 9.178779875 + 0.5 x = 9.178779875 + 0.5 Combine like terms: 9.178779875 + 0.5 = 9.678779875 x = 9.678779875 Simplifying x = 9.678779875

Subproblem 2

x + -0.5 = -9.178779875 Simplifying x + -0.5 = -9.178779875 Reorder the terms: -0.5 + x = -9.178779875 Solving -0.5 + x = -9.178779875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -9.178779875 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -9.178779875 + 0.5 x = -9.178779875 + 0.5 Combine like terms: -9.178779875 + 0.5 = -8.678779875 x = -8.678779875 Simplifying x = -8.678779875

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.678779875, -8.678779875}

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