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Simplifying -4w2 + 5w + 4 = 0 Reorder the terms: 4 + 5w + -4w2 = 0 Solving 4 + 5w + -4w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -1 + -1.25w + w2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -1.25w + 1 + w2 = 0 + 1 Reorder the terms: -1 + 1 + -1.25w + w2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1.25w + w2 = 0 + 1 -1.25w + w2 = 0 + 1 Combine like terms: 0 + 1 = 1 -1.25w + w2 = 1 The w term is -1.25w. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25w + 0.390625 + w2 = 1 + 0.390625 Reorder the terms: 0.390625 + -1.25w + w2 = 1 + 0.390625 Combine like terms: 1 + 0.390625 = 1.390625 0.390625 + -1.25w + w2 = 1.390625 Factor a perfect square on the left side: (w + -0.625)(w + -0.625) = 1.390625 Calculate the square root of the right side: 1.179247642 Break this problem into two subproblems by setting (w + -0.625) equal to 1.179247642 and -1.179247642.Subproblem 1
w + -0.625 = 1.179247642 Simplifying w + -0.625 = 1.179247642 Reorder the terms: -0.625 + w = 1.179247642 Solving -0.625 + w = 1.179247642 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + w = 1.179247642 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + w = 1.179247642 + 0.625 w = 1.179247642 + 0.625 Combine like terms: 1.179247642 + 0.625 = 1.804247642 w = 1.804247642 Simplifying w = 1.804247642Subproblem 2
w + -0.625 = -1.179247642 Simplifying w + -0.625 = -1.179247642 Reorder the terms: -0.625 + w = -1.179247642 Solving -0.625 + w = -1.179247642 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + w = -1.179247642 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + w = -1.179247642 + 0.625 w = -1.179247642 + 0.625 Combine like terms: -1.179247642 + 0.625 = -0.554247642 w = -0.554247642 Simplifying w = -0.554247642Solution
The solution to the problem is based on the solutions from the subproblems. w = {1.804247642, -0.554247642}
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