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Simplifying 16 = w(2w + -1.4) Reorder the terms: 16 = w(-1.4 + 2w) 16 = (-1.4 * w + 2w * w) 16 = (-1.4w + 2w2) Solving 16 = -1.4w + 2w2 Solving for variable 'w'. Reorder the terms: 16 + 1.4w + -2w2 = -1.4w + 1.4w + 2w2 + -2w2 Combine like terms: -1.4w + 1.4w = 0.0 16 + 1.4w + -2w2 = 0.0 + 2w2 + -2w2 16 + 1.4w + -2w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 16 + 1.4w + -2w2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -8 + -0.7w + w2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + -0.7w + 8 + w2 = 0 + 8 Reorder the terms: -8 + 8 + -0.7w + w2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -0.7w + w2 = 0 + 8 -0.7w + w2 = 0 + 8 Combine like terms: 0 + 8 = 8 -0.7w + w2 = 8 The w term is -0.7w. Take half its coefficient (-0.35). Square it (0.1225) and add it to both sides. Add '0.1225' to each side of the equation. -0.7w + 0.1225 + w2 = 8 + 0.1225 Reorder the terms: 0.1225 + -0.7w + w2 = 8 + 0.1225 Combine like terms: 8 + 0.1225 = 8.1225 0.1225 + -0.7w + w2 = 8.1225 Factor a perfect square on the left side: (w + -0.35)(w + -0.35) = 8.1225 Calculate the square root of the right side: 2.85 Break this problem into two subproblems by setting (w + -0.35) equal to 2.85 and -2.85.Subproblem 1
w + -0.35 = 2.85 Simplifying w + -0.35 = 2.85 Reorder the terms: -0.35 + w = 2.85 Solving -0.35 + w = 2.85 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.35' to each side of the equation. -0.35 + 0.35 + w = 2.85 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + w = 2.85 + 0.35 w = 2.85 + 0.35 Combine like terms: 2.85 + 0.35 = 3.2 w = 3.2 Simplifying w = 3.2Subproblem 2
w + -0.35 = -2.85 Simplifying w + -0.35 = -2.85 Reorder the terms: -0.35 + w = -2.85 Solving -0.35 + w = -2.85 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.35' to each side of the equation. -0.35 + 0.35 + w = -2.85 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + w = -2.85 + 0.35 w = -2.85 + 0.35 Combine like terms: -2.85 + 0.35 = -2.5 w = -2.5 Simplifying w = -2.5Solution
The solution to the problem is based on the solutions from the subproblems. w = {3.2, -2.5}
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