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