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Simplifying 2w2 + -1w2 + -1w + -9 = 0 Reorder the terms: -9 + -1w + 2w2 + -1w2 = 0 Combine like terms: 2w2 + -1w2 = 1w2 -9 + -1w + 1w2 = 0 Solving -9 + -1w + 1w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -1w + 9 + w2 = 0 + 9 Reorder the terms: -9 + 9 + -1w + w2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1w + w2 = 0 + 9 -1w + w2 = 0 + 9 Combine like terms: 0 + 9 = 9 -1w + w2 = 9 The w term is -1w. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1w + 0.25 + w2 = 9 + 0.25 Reorder the terms: 0.25 + -1w + w2 = 9 + 0.25 Combine like terms: 9 + 0.25 = 9.25 0.25 + -1w + w2 = 9.25 Factor a perfect square on the left side: (w + -0.5)(w + -0.5) = 9.25 Calculate the square root of the right side: 3.041381265 Break this problem into two subproblems by setting (w + -0.5) equal to 3.041381265 and -3.041381265.Subproblem 1
w + -0.5 = 3.041381265 Simplifying w + -0.5 = 3.041381265 Reorder the terms: -0.5 + w = 3.041381265 Solving -0.5 + w = 3.041381265 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + w = 3.041381265 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + w = 3.041381265 + 0.5 w = 3.041381265 + 0.5 Combine like terms: 3.041381265 + 0.5 = 3.541381265 w = 3.541381265 Simplifying w = 3.541381265Subproblem 2
w + -0.5 = -3.041381265 Simplifying w + -0.5 = -3.041381265 Reorder the terms: -0.5 + w = -3.041381265 Solving -0.5 + w = -3.041381265 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + w = -3.041381265 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + w = -3.041381265 + 0.5 w = -3.041381265 + 0.5 Combine like terms: -3.041381265 + 0.5 = -2.541381265 w = -2.541381265 Simplifying w = -2.541381265Solution
The solution to the problem is based on the solutions from the subproblems. w = {3.541381265, -2.541381265}
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