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Simplifying 2w2 + -9w + -70 = 0 Reorder the terms: -70 + -9w + 2w2 = 0 Solving -70 + -9w + 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'. -35 + -4.5w + w2 = 0 Move the constant term to the right: Add '35' to each side of the equation. -35 + -4.5w + 35 + w2 = 0 + 35 Reorder the terms: -35 + 35 + -4.5w + w2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + -4.5w + w2 = 0 + 35 -4.5w + w2 = 0 + 35 Combine like terms: 0 + 35 = 35 -4.5w + w2 = 35 The w term is -4.5w. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5w + 5.0625 + w2 = 35 + 5.0625 Reorder the terms: 5.0625 + -4.5w + w2 = 35 + 5.0625 Combine like terms: 35 + 5.0625 = 40.0625 5.0625 + -4.5w + w2 = 40.0625 Factor a perfect square on the left side: (w + -2.25)(w + -2.25) = 40.0625 Calculate the square root of the right side: 6.329494451 Break this problem into two subproblems by setting (w + -2.25) equal to 6.329494451 and -6.329494451.Subproblem 1
w + -2.25 = 6.329494451 Simplifying w + -2.25 = 6.329494451 Reorder the terms: -2.25 + w = 6.329494451 Solving -2.25 + w = 6.329494451 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + w = 6.329494451 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + w = 6.329494451 + 2.25 w = 6.329494451 + 2.25 Combine like terms: 6.329494451 + 2.25 = 8.579494451 w = 8.579494451 Simplifying w = 8.579494451Subproblem 2
w + -2.25 = -6.329494451 Simplifying w + -2.25 = -6.329494451 Reorder the terms: -2.25 + w = -6.329494451 Solving -2.25 + w = -6.329494451 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + w = -6.329494451 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + w = -6.329494451 + 2.25 w = -6.329494451 + 2.25 Combine like terms: -6.329494451 + 2.25 = -4.079494451 w = -4.079494451 Simplifying w = -4.079494451Solution
The solution to the problem is based on the solutions from the subproblems. w = {8.579494451, -4.079494451}
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