x^2-17x+31=0

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Solution for x^2-17x+31=0 equation:


Simplifying
x2 + -17x + 31 = 0

Reorder the terms:
31 + -17x + x2 = 0

Solving
31 + -17x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-31' to each side of the equation.
31 + -17x + -31 + x2 = 0 + -31

Reorder the terms:
31 + -31 + -17x + x2 = 0 + -31

Combine like terms: 31 + -31 = 0
0 + -17x + x2 = 0 + -31
-17x + x2 = 0 + -31

Combine like terms: 0 + -31 = -31
-17x + x2 = -31

The x term is -17x.  Take half its coefficient (-8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
-17x + 72.25 + x2 = -31 + 72.25

Reorder the terms:
72.25 + -17x + x2 = -31 + 72.25

Combine like terms: -31 + 72.25 = 41.25
72.25 + -17x + x2 = 41.25

Factor a perfect square on the left side:
(x + -8.5)(x + -8.5) = 41.25

Calculate the square root of the right side: 6.422616289

Break this problem into two subproblems by setting 
(x + -8.5) equal to 6.422616289 and -6.422616289.

Subproblem 1

x + -8.5 = 6.422616289 Simplifying x + -8.5 = 6.422616289 Reorder the terms: -8.5 + x = 6.422616289 Solving -8.5 + x = 6.422616289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = 6.422616289 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 6.422616289 + 8.5 x = 6.422616289 + 8.5 Combine like terms: 6.422616289 + 8.5 = 14.922616289 x = 14.922616289 Simplifying x = 14.922616289

Subproblem 2

x + -8.5 = -6.422616289 Simplifying x + -8.5 = -6.422616289 Reorder the terms: -8.5 + x = -6.422616289 Solving -8.5 + x = -6.422616289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = -6.422616289 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -6.422616289 + 8.5 x = -6.422616289 + 8.5 Combine like terms: -6.422616289 + 8.5 = 2.077383711 x = 2.077383711 Simplifying x = 2.077383711

Solution

The solution to the problem is based on the solutions from the subproblems. x = {14.922616289, 2.077383711}

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