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Simplifying 6w2 + -3w + -15 = 0 Reorder the terms: -15 + -3w + 6w2 = 0 Solving -15 + -3w + 6w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '3'. 3(-5 + -1w + 2w2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-5 + -1w + 2w2)' equal to zero and attempt to solve: Simplifying -5 + -1w + 2w2 = 0 Solving -5 + -1w + 2w2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2.5 + -0.5w + w2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -0.5w + 2.5 + w2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -0.5w + w2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -0.5w + w2 = 0 + 2.5 -0.5w + w2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -0.5w + w2 = 2.5 The w term is -0.5w. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5w + 0.0625 + w2 = 2.5 + 0.0625 Reorder the terms: 0.0625 + -0.5w + w2 = 2.5 + 0.0625 Combine like terms: 2.5 + 0.0625 = 2.5625 0.0625 + -0.5w + w2 = 2.5625 Factor a perfect square on the left side: (w + -0.25)(w + -0.25) = 2.5625 Calculate the square root of the right side: 1.600781059 Break this problem into two subproblems by setting (w + -0.25) equal to 1.600781059 and -1.600781059.Subproblem 1
w + -0.25 = 1.600781059 Simplifying w + -0.25 = 1.600781059 Reorder the terms: -0.25 + w = 1.600781059 Solving -0.25 + w = 1.600781059 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + w = 1.600781059 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + w = 1.600781059 + 0.25 w = 1.600781059 + 0.25 Combine like terms: 1.600781059 + 0.25 = 1.850781059 w = 1.850781059 Simplifying w = 1.850781059Subproblem 2
w + -0.25 = -1.600781059 Simplifying w + -0.25 = -1.600781059 Reorder the terms: -0.25 + w = -1.600781059 Solving -0.25 + w = -1.600781059 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + w = -1.600781059 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + w = -1.600781059 + 0.25 w = -1.600781059 + 0.25 Combine like terms: -1.600781059 + 0.25 = -1.350781059 w = -1.350781059 Simplifying w = -1.350781059Solution
The solution to the problem is based on the solutions from the subproblems. w = {1.850781059, -1.350781059}Solution
w = {1.850781059, -1.350781059}
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