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Simplifying 15 = w2 + 4w Reorder the terms: 15 = 4w + w2 Solving 15 = 4w + w2 Solving for variable 'w'. Reorder the terms: 15 + -4w + -1w2 = 4w + -4w + w2 + -1w2 Combine like terms: 4w + -4w = 0 15 + -4w + -1w2 = 0 + w2 + -1w2 15 + -4w + -1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 15 + -4w + -1w2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -15 + 4w + w2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + 4w + 15 + w2 = 0 + 15 Reorder the terms: -15 + 15 + 4w + w2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 4w + w2 = 0 + 15 4w + w2 = 0 + 15 Combine like terms: 0 + 15 = 15 4w + w2 = 15 The w term is 4w. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4w + 4 + w2 = 15 + 4 Reorder the terms: 4 + 4w + w2 = 15 + 4 Combine like terms: 15 + 4 = 19 4 + 4w + w2 = 19 Factor a perfect square on the left side: (w + 2)(w + 2) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (w + 2) equal to 4.358898944 and -4.358898944.Subproblem 1
w + 2 = 4.358898944 Simplifying w + 2 = 4.358898944 Reorder the terms: 2 + w = 4.358898944 Solving 2 + w = 4.358898944 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + w = 4.358898944 + -2 Combine like terms: 2 + -2 = 0 0 + w = 4.358898944 + -2 w = 4.358898944 + -2 Combine like terms: 4.358898944 + -2 = 2.358898944 w = 2.358898944 Simplifying w = 2.358898944Subproblem 2
w + 2 = -4.358898944 Simplifying w + 2 = -4.358898944 Reorder the terms: 2 + w = -4.358898944 Solving 2 + w = -4.358898944 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + w = -4.358898944 + -2 Combine like terms: 2 + -2 = 0 0 + w = -4.358898944 + -2 w = -4.358898944 + -2 Combine like terms: -4.358898944 + -2 = -6.358898944 w = -6.358898944 Simplifying w = -6.358898944Solution
The solution to the problem is based on the solutions from the subproblems. w = {2.358898944, -6.358898944}
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