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Simplifying 4w2 + -1w + -29 = 0 Reorder the terms: -29 + -1w + 4w2 = 0 Solving -29 + -1w + 4w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -7.25 + -0.25w + w2 = 0 Move the constant term to the right: Add '7.25' to each side of the equation. -7.25 + -0.25w + 7.25 + w2 = 0 + 7.25 Reorder the terms: -7.25 + 7.25 + -0.25w + w2 = 0 + 7.25 Combine like terms: -7.25 + 7.25 = 0.00 0.00 + -0.25w + w2 = 0 + 7.25 -0.25w + w2 = 0 + 7.25 Combine like terms: 0 + 7.25 = 7.25 -0.25w + w2 = 7.25 The w term is -0.25w. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25w + 0.015625 + w2 = 7.25 + 0.015625 Reorder the terms: 0.015625 + -0.25w + w2 = 7.25 + 0.015625 Combine like terms: 7.25 + 0.015625 = 7.265625 0.015625 + -0.25w + w2 = 7.265625 Factor a perfect square on the left side: (w + -0.125)(w + -0.125) = 7.265625 Calculate the square root of the right side: 2.695482332 Break this problem into two subproblems by setting (w + -0.125) equal to 2.695482332 and -2.695482332.Subproblem 1
w + -0.125 = 2.695482332 Simplifying w + -0.125 = 2.695482332 Reorder the terms: -0.125 + w = 2.695482332 Solving -0.125 + w = 2.695482332 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + w = 2.695482332 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + w = 2.695482332 + 0.125 w = 2.695482332 + 0.125 Combine like terms: 2.695482332 + 0.125 = 2.820482332 w = 2.820482332 Simplifying w = 2.820482332Subproblem 2
w + -0.125 = -2.695482332 Simplifying w + -0.125 = -2.695482332 Reorder the terms: -0.125 + w = -2.695482332 Solving -0.125 + w = -2.695482332 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + w = -2.695482332 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + w = -2.695482332 + 0.125 w = -2.695482332 + 0.125 Combine like terms: -2.695482332 + 0.125 = -2.570482332 w = -2.570482332 Simplifying w = -2.570482332Solution
The solution to the problem is based on the solutions from the subproblems. w = {2.820482332, -2.570482332}
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