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Simplifying 4w2 + -5w = 50 Reorder the terms: -5w + 4w2 = 50 Solving -5w + 4w2 = 50 Solving for variable 'w'. Reorder the terms: -50 + -5w + 4w2 = 50 + -50 Combine like terms: 50 + -50 = 0 -50 + -5w + 4w2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -12.5 + -1.25w + w2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + -1.25w + 12.5 + w2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + -1.25w + w2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + -1.25w + w2 = 0 + 12.5 -1.25w + w2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 -1.25w + w2 = 12.5 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 = 12.5 + 0.390625 Reorder the terms: 0.390625 + -1.25w + w2 = 12.5 + 0.390625 Combine like terms: 12.5 + 0.390625 = 12.890625 0.390625 + -1.25w + w2 = 12.890625 Factor a perfect square on the left side: (w + -0.625)(w + -0.625) = 12.890625 Calculate the square root of the right side: 3.590351654 Break this problem into two subproblems by setting (w + -0.625) equal to 3.590351654 and -3.590351654.Subproblem 1
w + -0.625 = 3.590351654 Simplifying w + -0.625 = 3.590351654 Reorder the terms: -0.625 + w = 3.590351654 Solving -0.625 + w = 3.590351654 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 = 3.590351654 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + w = 3.590351654 + 0.625 w = 3.590351654 + 0.625 Combine like terms: 3.590351654 + 0.625 = 4.215351654 w = 4.215351654 Simplifying w = 4.215351654Subproblem 2
w + -0.625 = -3.590351654 Simplifying w + -0.625 = -3.590351654 Reorder the terms: -0.625 + w = -3.590351654 Solving -0.625 + w = -3.590351654 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 = -3.590351654 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + w = -3.590351654 + 0.625 w = -3.590351654 + 0.625 Combine like terms: -3.590351654 + 0.625 = -2.965351654 w = -2.965351654 Simplifying w = -2.965351654Solution
The solution to the problem is based on the solutions from the subproblems. w = {4.215351654, -2.965351654}
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