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Simplifying -2w2 + -50w + 84 = 0 Reorder the terms: 84 + -50w + -2w2 = 0 Solving 84 + -50w + -2w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2'. 2(42 + -25w + -1w2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(42 + -25w + -1w2)' equal to zero and attempt to solve: Simplifying 42 + -25w + -1w2 = 0 Solving 42 + -25w + -1w2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -42 + 25w + w2 = 0 Move the constant term to the right: Add '42' to each side of the equation. -42 + 25w + 42 + w2 = 0 + 42 Reorder the terms: -42 + 42 + 25w + w2 = 0 + 42 Combine like terms: -42 + 42 = 0 0 + 25w + w2 = 0 + 42 25w + w2 = 0 + 42 Combine like terms: 0 + 42 = 42 25w + w2 = 42 The w term is 25w. Take half its coefficient (12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. 25w + 156.25 + w2 = 42 + 156.25 Reorder the terms: 156.25 + 25w + w2 = 42 + 156.25 Combine like terms: 42 + 156.25 = 198.25 156.25 + 25w + w2 = 198.25 Factor a perfect square on the left side: (w + 12.5)(w + 12.5) = 198.25 Calculate the square root of the right side: 14.08012784 Break this problem into two subproblems by setting (w + 12.5) equal to 14.08012784 and -14.08012784.Subproblem 1
w + 12.5 = 14.08012784 Simplifying w + 12.5 = 14.08012784 Reorder the terms: 12.5 + w = 14.08012784 Solving 12.5 + w = 14.08012784 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + w = 14.08012784 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + w = 14.08012784 + -12.5 w = 14.08012784 + -12.5 Combine like terms: 14.08012784 + -12.5 = 1.58012784 w = 1.58012784 Simplifying w = 1.58012784Subproblem 2
w + 12.5 = -14.08012784 Simplifying w + 12.5 = -14.08012784 Reorder the terms: 12.5 + w = -14.08012784 Solving 12.5 + w = -14.08012784 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + w = -14.08012784 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + w = -14.08012784 + -12.5 w = -14.08012784 + -12.5 Combine like terms: -14.08012784 + -12.5 = -26.58012784 w = -26.58012784 Simplifying w = -26.58012784Solution
The solution to the problem is based on the solutions from the subproblems. w = {1.58012784, -26.58012784}Solution
w = {1.58012784, -26.58012784}
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