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Simplifying -3w2 + -75w + -6 = 0 Reorder the terms: -6 + -75w + -3w2 = 0 Solving -6 + -75w + -3w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '-3'. -3(2 + 25w + w2) = 0 Ignore the factor -3.Subproblem 1
Set the factor '(2 + 25w + w2)' equal to zero and attempt to solve: Simplifying 2 + 25w + w2 = 0 Solving 2 + 25w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + 25w + -2 + w2 = 0 + -2 Reorder the terms: 2 + -2 + 25w + w2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 25w + w2 = 0 + -2 25w + w2 = 0 + -2 Combine like terms: 0 + -2 = -2 25w + w2 = -2 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 = -2 + 156.25 Reorder the terms: 156.25 + 25w + w2 = -2 + 156.25 Combine like terms: -2 + 156.25 = 154.25 156.25 + 25w + w2 = 154.25 Factor a perfect square on the left side: (w + 12.5)(w + 12.5) = 154.25 Calculate the square root of the right side: 12.419742348 Break this problem into two subproblems by setting (w + 12.5) equal to 12.419742348 and -12.419742348.Subproblem 1
w + 12.5 = 12.419742348 Simplifying w + 12.5 = 12.419742348 Reorder the terms: 12.5 + w = 12.419742348 Solving 12.5 + w = 12.419742348 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 = 12.419742348 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + w = 12.419742348 + -12.5 w = 12.419742348 + -12.5 Combine like terms: 12.419742348 + -12.5 = -0.080257652 w = -0.080257652 Simplifying w = -0.080257652Subproblem 2
w + 12.5 = -12.419742348 Simplifying w + 12.5 = -12.419742348 Reorder the terms: 12.5 + w = -12.419742348 Solving 12.5 + w = -12.419742348 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 = -12.419742348 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + w = -12.419742348 + -12.5 w = -12.419742348 + -12.5 Combine like terms: -12.419742348 + -12.5 = -24.919742348 w = -24.919742348 Simplifying w = -24.919742348Solution
The solution to the problem is based on the solutions from the subproblems. w = {-0.080257652, -24.919742348}Solution
w = {-0.080257652, -24.919742348}
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