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Simplifying -1w(4w + -3) = -12 Reorder the terms: -1w(-3 + 4w) = -12 (-3 * -1w + 4w * -1w) = -12 (3w + -4w2) = -12 Solving 3w + -4w2 = -12 Solving for variable 'w'. Reorder the terms: 12 + 3w + -4w2 = -12 + 12 Combine like terms: -12 + 12 = 0 12 + 3w + -4w2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -3 + -0.75w + w2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -0.75w + 3 + w2 = 0 + 3 Reorder the terms: -3 + 3 + -0.75w + w2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -0.75w + w2 = 0 + 3 -0.75w + w2 = 0 + 3 Combine like terms: 0 + 3 = 3 -0.75w + w2 = 3 The w term is -0.75w. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75w + 0.140625 + w2 = 3 + 0.140625 Reorder the terms: 0.140625 + -0.75w + w2 = 3 + 0.140625 Combine like terms: 3 + 0.140625 = 3.140625 0.140625 + -0.75w + w2 = 3.140625 Factor a perfect square on the left side: (w + -0.375)(w + -0.375) = 3.140625 Calculate the square root of the right side: 1.77218086 Break this problem into two subproblems by setting (w + -0.375) equal to 1.77218086 and -1.77218086.Subproblem 1
w + -0.375 = 1.77218086 Simplifying w + -0.375 = 1.77218086 Reorder the terms: -0.375 + w = 1.77218086 Solving -0.375 + w = 1.77218086 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + w = 1.77218086 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + w = 1.77218086 + 0.375 w = 1.77218086 + 0.375 Combine like terms: 1.77218086 + 0.375 = 2.14718086 w = 2.14718086 Simplifying w = 2.14718086Subproblem 2
w + -0.375 = -1.77218086 Simplifying w + -0.375 = -1.77218086 Reorder the terms: -0.375 + w = -1.77218086 Solving -0.375 + w = -1.77218086 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + w = -1.77218086 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + w = -1.77218086 + 0.375 w = -1.77218086 + 0.375 Combine like terms: -1.77218086 + 0.375 = -1.39718086 w = -1.39718086 Simplifying w = -1.39718086Solution
The solution to the problem is based on the solutions from the subproblems. w = {2.14718086, -1.39718086}
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