w^2+5w-133=0

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Solution for w^2+5w-133=0 equation:


Simplifying
w2 + 5w + -133 = 0

Reorder the terms:
-133 + 5w + w2 = 0

Solving
-133 + 5w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '133' to each side of the equation.
-133 + 5w + 133 + w2 = 0 + 133

Reorder the terms:
-133 + 133 + 5w + w2 = 0 + 133

Combine like terms: -133 + 133 = 0
0 + 5w + w2 = 0 + 133
5w + w2 = 0 + 133

Combine like terms: 0 + 133 = 133
5w + w2 = 133

The w term is 5w.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5w + 6.25 + w2 = 133 + 6.25

Reorder the terms:
6.25 + 5w + w2 = 133 + 6.25

Combine like terms: 133 + 6.25 = 139.25
6.25 + 5w + w2 = 139.25

Factor a perfect square on the left side:
(w + 2.5)(w + 2.5) = 139.25

Calculate the square root of the right side: 11.800423721

Break this problem into two subproblems by setting 
(w + 2.5) equal to 11.800423721 and -11.800423721.

Subproblem 1

w + 2.5 = 11.800423721 Simplifying w + 2.5 = 11.800423721 Reorder the terms: 2.5 + w = 11.800423721 Solving 2.5 + w = 11.800423721 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + w = 11.800423721 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + w = 11.800423721 + -2.5 w = 11.800423721 + -2.5 Combine like terms: 11.800423721 + -2.5 = 9.300423721 w = 9.300423721 Simplifying w = 9.300423721

Subproblem 2

w + 2.5 = -11.800423721 Simplifying w + 2.5 = -11.800423721 Reorder the terms: 2.5 + w = -11.800423721 Solving 2.5 + w = -11.800423721 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + w = -11.800423721 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + w = -11.800423721 + -2.5 w = -11.800423721 + -2.5 Combine like terms: -11.800423721 + -2.5 = -14.300423721 w = -14.300423721 Simplifying w = -14.300423721

Solution

The solution to the problem is based on the solutions from the subproblems. w = {9.300423721, -14.300423721}

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