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Simplifying 40 = w2 + 13w Reorder the terms: 40 = 13w + w2 Solving 40 = 13w + w2 Solving for variable 'w'. Reorder the terms: 40 + -13w + -1w2 = 13w + -13w + w2 + -1w2 Combine like terms: 13w + -13w = 0 40 + -13w + -1w2 = 0 + w2 + -1w2 40 + -13w + -1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 40 + -13w + -1w2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -40 + 13w + w2 = 0 Move the constant term to the right: Add '40' to each side of the equation. -40 + 13w + 40 + w2 = 0 + 40 Reorder the terms: -40 + 40 + 13w + w2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + 13w + w2 = 0 + 40 13w + w2 = 0 + 40 Combine like terms: 0 + 40 = 40 13w + w2 = 40 The w term is 13w. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13w + 42.25 + w2 = 40 + 42.25 Reorder the terms: 42.25 + 13w + w2 = 40 + 42.25 Combine like terms: 40 + 42.25 = 82.25 42.25 + 13w + w2 = 82.25 Factor a perfect square on the left side: (w + 6.5)(w + 6.5) = 82.25 Calculate the square root of the right side: 9.069178574 Break this problem into two subproblems by setting (w + 6.5) equal to 9.069178574 and -9.069178574.Subproblem 1
w + 6.5 = 9.069178574 Simplifying w + 6.5 = 9.069178574 Reorder the terms: 6.5 + w = 9.069178574 Solving 6.5 + w = 9.069178574 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + w = 9.069178574 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + w = 9.069178574 + -6.5 w = 9.069178574 + -6.5 Combine like terms: 9.069178574 + -6.5 = 2.569178574 w = 2.569178574 Simplifying w = 2.569178574Subproblem 2
w + 6.5 = -9.069178574 Simplifying w + 6.5 = -9.069178574 Reorder the terms: 6.5 + w = -9.069178574 Solving 6.5 + w = -9.069178574 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + w = -9.069178574 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + w = -9.069178574 + -6.5 w = -9.069178574 + -6.5 Combine like terms: -9.069178574 + -6.5 = -15.569178574 w = -15.569178574 Simplifying w = -15.569178574Solution
The solution to the problem is based on the solutions from the subproblems. w = {2.569178574, -15.569178574}
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