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Simplifying 2w2 + -1w + -30 = 0 Reorder the terms: -30 + -1w + 2w2 = 0 Solving -30 + -1w + 2w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -15 + -0.5w + w2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + -0.5w + 15 + w2 = 0 + 15 Reorder the terms: -15 + 15 + -0.5w + w2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -0.5w + w2 = 0 + 15 -0.5w + w2 = 0 + 15 Combine like terms: 0 + 15 = 15 -0.5w + w2 = 15 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 = 15 + 0.0625 Reorder the terms: 0.0625 + -0.5w + w2 = 15 + 0.0625 Combine like terms: 15 + 0.0625 = 15.0625 0.0625 + -0.5w + w2 = 15.0625 Factor a perfect square on the left side: (w + -0.25)(w + -0.25) = 15.0625 Calculate the square root of the right side: 3.881043674 Break this problem into two subproblems by setting (w + -0.25) equal to 3.881043674 and -3.881043674.Subproblem 1
w + -0.25 = 3.881043674 Simplifying w + -0.25 = 3.881043674 Reorder the terms: -0.25 + w = 3.881043674 Solving -0.25 + w = 3.881043674 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 = 3.881043674 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + w = 3.881043674 + 0.25 w = 3.881043674 + 0.25 Combine like terms: 3.881043674 + 0.25 = 4.131043674 w = 4.131043674 Simplifying w = 4.131043674Subproblem 2
w + -0.25 = -3.881043674 Simplifying w + -0.25 = -3.881043674 Reorder the terms: -0.25 + w = -3.881043674 Solving -0.25 + w = -3.881043674 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 = -3.881043674 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + w = -3.881043674 + 0.25 w = -3.881043674 + 0.25 Combine like terms: -3.881043674 + 0.25 = -3.631043674 w = -3.631043674 Simplifying w = -3.631043674Solution
The solution to the problem is based on the solutions from the subproblems. w = {4.131043674, -3.631043674}
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