w^2+7w=28

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Solution for w^2+7w=28 equation:


Simplifying
w2 + 7w = 28

Reorder the terms:
7w + w2 = 28

Solving
7w + w2 = 28

Solving for variable 'w'.

Reorder the terms:
-28 + 7w + w2 = 28 + -28

Combine like terms: 28 + -28 = 0
-28 + 7w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '28' to each side of the equation.
-28 + 7w + 28 + w2 = 0 + 28

Reorder the terms:
-28 + 28 + 7w + w2 = 0 + 28

Combine like terms: -28 + 28 = 0
0 + 7w + w2 = 0 + 28
7w + w2 = 0 + 28

Combine like terms: 0 + 28 = 28
7w + w2 = 28

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 = 28 + 12.25

Reorder the terms:
12.25 + 7w + w2 = 28 + 12.25

Combine like terms: 28 + 12.25 = 40.25
12.25 + 7w + w2 = 40.25

Factor a perfect square on the left side:
(w + 3.5)(w + 3.5) = 40.25

Calculate the square root of the right side: 6.34428877

Break this problem into two subproblems by setting 
(w + 3.5) equal to 6.34428877 and -6.34428877.

Subproblem 1

w + 3.5 = 6.34428877 Simplifying w + 3.5 = 6.34428877 Reorder the terms: 3.5 + w = 6.34428877 Solving 3.5 + w = 6.34428877 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 = 6.34428877 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + w = 6.34428877 + -3.5 w = 6.34428877 + -3.5 Combine like terms: 6.34428877 + -3.5 = 2.84428877 w = 2.84428877 Simplifying w = 2.84428877

Subproblem 2

w + 3.5 = -6.34428877 Simplifying w + 3.5 = -6.34428877 Reorder the terms: 3.5 + w = -6.34428877 Solving 3.5 + w = -6.34428877 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 = -6.34428877 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + w = -6.34428877 + -3.5 w = -6.34428877 + -3.5 Combine like terms: -6.34428877 + -3.5 = -9.84428877 w = -9.84428877 Simplifying w = -9.84428877

Solution

The solution to the problem is based on the solutions from the subproblems. w = {2.84428877, -9.84428877}

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