w^2+7w=90

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Solution for w^2+7w=90 equation:


Simplifying
w2 + 7w = 90

Reorder the terms:
7w + w2 = 90

Solving
7w + w2 = 90

Solving for variable 'w'.

Reorder the terms:
-90 + 7w + w2 = 90 + -90

Combine like terms: 90 + -90 = 0
-90 + 7w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '90' to each side of the equation.
-90 + 7w + 90 + w2 = 0 + 90

Reorder the terms:
-90 + 90 + 7w + w2 = 0 + 90

Combine like terms: -90 + 90 = 0
0 + 7w + w2 = 0 + 90
7w + w2 = 0 + 90

Combine like terms: 0 + 90 = 90
7w + w2 = 90

The w term is 7w.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7w + 12.25 + w2 = 90 + 12.25

Reorder the terms:
12.25 + 7w + w2 = 90 + 12.25

Combine like terms: 90 + 12.25 = 102.25
12.25 + 7w + w2 = 102.25

Factor a perfect square on the left side:
(w + 3.5)(w + 3.5) = 102.25

Calculate the square root of the right side: 10.111874208

Break this problem into two subproblems by setting 
(w + 3.5) equal to 10.111874208 and -10.111874208.

Subproblem 1

w + 3.5 = 10.111874208 Simplifying w + 3.5 = 10.111874208 Reorder the terms: 3.5 + w = 10.111874208 Solving 3.5 + w = 10.111874208 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + w = 10.111874208 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + w = 10.111874208 + -3.5 w = 10.111874208 + -3.5 Combine like terms: 10.111874208 + -3.5 = 6.611874208 w = 6.611874208 Simplifying w = 6.611874208

Subproblem 2

w + 3.5 = -10.111874208 Simplifying w + 3.5 = -10.111874208 Reorder the terms: 3.5 + w = -10.111874208 Solving 3.5 + w = -10.111874208 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + w = -10.111874208 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + w = -10.111874208 + -3.5 w = -10.111874208 + -3.5 Combine like terms: -10.111874208 + -3.5 = -13.611874208 w = -13.611874208 Simplifying w = -13.611874208

Solution

The solution to the problem is based on the solutions from the subproblems. w = {6.611874208, -13.611874208}

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