x^2-x-2=32.5

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Solution for x^2-x-2=32.5 equation:


Simplifying
x2 + -1x + -2 = 32.5

Reorder the terms:
-2 + -1x + x2 = 32.5

Solving
-2 + -1x + x2 = 32.5

Solving for variable 'x'.

Reorder the terms:
-2 + -32.5 + -1x + x2 = 32.5 + -32.5

Combine like terms: -2 + -32.5 = -34.5
-34.5 + -1x + x2 = 32.5 + -32.5

Combine like terms: 32.5 + -32.5 = 0.0
-34.5 + -1x + x2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '34.5' to each side of the equation.
-34.5 + -1x + 34.5 + x2 = 0.0 + 34.5

Reorder the terms:
-34.5 + 34.5 + -1x + x2 = 0.0 + 34.5

Combine like terms: -34.5 + 34.5 = 0.0
0.0 + -1x + x2 = 0.0 + 34.5
-1x + x2 = 0.0 + 34.5

Combine like terms: 0.0 + 34.5 = 34.5
-1x + x2 = 34.5

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 = 34.5 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 34.5 + 0.25

Combine like terms: 34.5 + 0.25 = 34.75
0.25 + -1x + x2 = 34.75

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 34.75

Calculate the square root of the right side: 5.894913061

Break this problem into two subproblems by setting 
(x + -0.5) equal to 5.894913061 and -5.894913061.

Subproblem 1

x + -0.5 = 5.894913061 Simplifying x + -0.5 = 5.894913061 Reorder the terms: -0.5 + x = 5.894913061 Solving -0.5 + x = 5.894913061 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 = 5.894913061 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 5.894913061 + 0.5 x = 5.894913061 + 0.5 Combine like terms: 5.894913061 + 0.5 = 6.394913061 x = 6.394913061 Simplifying x = 6.394913061

Subproblem 2

x + -0.5 = -5.894913061 Simplifying x + -0.5 = -5.894913061 Reorder the terms: -0.5 + x = -5.894913061 Solving -0.5 + x = -5.894913061 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 = -5.894913061 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -5.894913061 + 0.5 x = -5.894913061 + 0.5 Combine like terms: -5.894913061 + 0.5 = -5.394913061 x = -5.394913061 Simplifying x = -5.394913061

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.394913061, -5.394913061}

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