w^2-6w-31=0

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Solution for w^2-6w-31=0 equation:


Simplifying
w2 + -6w + -31 = 0

Reorder the terms:
-31 + -6w + w2 = 0

Solving
-31 + -6w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '31' to each side of the equation.
-31 + -6w + 31 + w2 = 0 + 31

Reorder the terms:
-31 + 31 + -6w + w2 = 0 + 31

Combine like terms: -31 + 31 = 0
0 + -6w + w2 = 0 + 31
-6w + w2 = 0 + 31

Combine like terms: 0 + 31 = 31
-6w + w2 = 31

The w term is -6w.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6w + 9 + w2 = 31 + 9

Reorder the terms:
9 + -6w + w2 = 31 + 9

Combine like terms: 31 + 9 = 40
9 + -6w + w2 = 40

Factor a perfect square on the left side:
(w + -3)(w + -3) = 40

Calculate the square root of the right side: 6.32455532

Break this problem into two subproblems by setting 
(w + -3) equal to 6.32455532 and -6.32455532.

Subproblem 1

w + -3 = 6.32455532 Simplifying w + -3 = 6.32455532 Reorder the terms: -3 + w = 6.32455532 Solving -3 + w = 6.32455532 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + w = 6.32455532 + 3 Combine like terms: -3 + 3 = 0 0 + w = 6.32455532 + 3 w = 6.32455532 + 3 Combine like terms: 6.32455532 + 3 = 9.32455532 w = 9.32455532 Simplifying w = 9.32455532

Subproblem 2

w + -3 = -6.32455532 Simplifying w + -3 = -6.32455532 Reorder the terms: -3 + w = -6.32455532 Solving -3 + w = -6.32455532 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + w = -6.32455532 + 3 Combine like terms: -3 + 3 = 0 0 + w = -6.32455532 + 3 w = -6.32455532 + 3 Combine like terms: -6.32455532 + 3 = -3.32455532 w = -3.32455532 Simplifying w = -3.32455532

Solution

The solution to the problem is based on the solutions from the subproblems. w = {9.32455532, -3.32455532}

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