x^2-23x-40=

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Solution for x^2-23x-40= equation:


Simplifying
x2 + -23x + -40 = 0

Reorder the terms:
-40 + -23x + x2 = 0

Solving
-40 + -23x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + -23x + 40 + x2 = 0 + 40

Reorder the terms:
-40 + 40 + -23x + x2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + -23x + x2 = 0 + 40
-23x + x2 = 0 + 40

Combine like terms: 0 + 40 = 40
-23x + x2 = 40

The x term is -23x.  Take half its coefficient (-11.5).
Square it (132.25) and add it to both sides.

Add '132.25' to each side of the equation.
-23x + 132.25 + x2 = 40 + 132.25

Reorder the terms:
132.25 + -23x + x2 = 40 + 132.25

Combine like terms: 40 + 132.25 = 172.25
132.25 + -23x + x2 = 172.25

Factor a perfect square on the left side:
(x + -11.5)(x + -11.5) = 172.25

Calculate the square root of the right side: 13.124404748

Break this problem into two subproblems by setting 
(x + -11.5) equal to 13.124404748 and -13.124404748.

Subproblem 1

x + -11.5 = 13.124404748 Simplifying x + -11.5 = 13.124404748 Reorder the terms: -11.5 + x = 13.124404748 Solving -11.5 + x = 13.124404748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + x = 13.124404748 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = 13.124404748 + 11.5 x = 13.124404748 + 11.5 Combine like terms: 13.124404748 + 11.5 = 24.624404748 x = 24.624404748 Simplifying x = 24.624404748

Subproblem 2

x + -11.5 = -13.124404748 Simplifying x + -11.5 = -13.124404748 Reorder the terms: -11.5 + x = -13.124404748 Solving -11.5 + x = -13.124404748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + x = -13.124404748 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = -13.124404748 + 11.5 x = -13.124404748 + 11.5 Combine like terms: -13.124404748 + 11.5 = -1.624404748 x = -1.624404748 Simplifying x = -1.624404748

Solution

The solution to the problem is based on the solutions from the subproblems. x = {24.624404748, -1.624404748}

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