43.75=w^2+15w

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Solution for 43.75=w^2+15w equation:


Simplifying
43.75 = w2 + 15w

Reorder the terms:
43.75 = 15w + w2

Solving
43.75 = 15w + w2

Solving for variable 'w'.

Reorder the terms:
43.75 + -15w + -1w2 = 15w + -15w + w2 + -1w2

Combine like terms: 15w + -15w = 0
43.75 + -15w + -1w2 = 0 + w2 + -1w2
43.75 + -15w + -1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
43.75 + -15w + -1w2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-43.75 + 15w + w2 = 0

Move the constant term to the right:

Add '43.75' to each side of the equation.
-43.75 + 15w + 43.75 + w2 = 0 + 43.75

Reorder the terms:
-43.75 + 43.75 + 15w + w2 = 0 + 43.75

Combine like terms: -43.75 + 43.75 = 0.00
0.00 + 15w + w2 = 0 + 43.75
15w + w2 = 0 + 43.75

Combine like terms: 0 + 43.75 = 43.75
15w + w2 = 43.75

The w term is 15w.  Take half its coefficient (7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
15w + 56.25 + w2 = 43.75 + 56.25

Reorder the terms:
56.25 + 15w + w2 = 43.75 + 56.25

Combine like terms: 43.75 + 56.25 = 100
56.25 + 15w + w2 = 100

Factor a perfect square on the left side:
(w + 7.5)(w + 7.5) = 100

Calculate the square root of the right side: 10

Break this problem into two subproblems by setting 
(w + 7.5) equal to 10 and -10.

Subproblem 1

w + 7.5 = 10 Simplifying w + 7.5 = 10 Reorder the terms: 7.5 + w = 10 Solving 7.5 + w = 10 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + w = 10 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + w = 10 + -7.5 w = 10 + -7.5 Combine like terms: 10 + -7.5 = 2.5 w = 2.5 Simplifying w = 2.5

Subproblem 2

w + 7.5 = -10 Simplifying w + 7.5 = -10 Reorder the terms: 7.5 + w = -10 Solving 7.5 + w = -10 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + w = -10 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + w = -10 + -7.5 w = -10 + -7.5 Combine like terms: -10 + -7.5 = -17.5 w = -17.5 Simplifying w = -17.5

Solution

The solution to the problem is based on the solutions from the subproblems. w = {2.5, -17.5}

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