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Simplifying 70 = 2w2 + 18w + -30 Reorder the terms: 70 = -30 + 18w + 2w2 Solving 70 = -30 + 18w + 2w2 Solving for variable 'w'. Combine like terms: 70 + 30 = 100 100 + -18w + -2w2 = -30 + 18w + 2w2 + 30 + -18w + -2w2 Reorder the terms: 100 + -18w + -2w2 = -30 + 30 + 18w + -18w + 2w2 + -2w2 Combine like terms: -30 + 30 = 0 100 + -18w + -2w2 = 0 + 18w + -18w + 2w2 + -2w2 100 + -18w + -2w2 = 18w + -18w + 2w2 + -2w2 Combine like terms: 18w + -18w = 0 100 + -18w + -2w2 = 0 + 2w2 + -2w2 100 + -18w + -2w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 100 + -18w + -2w2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(50 + -9w + -1w2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(50 + -9w + -1w2)' equal to zero and attempt to solve: Simplifying 50 + -9w + -1w2 = 0 Solving 50 + -9w + -1w2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -50 + 9w + w2 = 0 Move the constant term to the right: Add '50' to each side of the equation. -50 + 9w + 50 + w2 = 0 + 50 Reorder the terms: -50 + 50 + 9w + w2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + 9w + w2 = 0 + 50 9w + w2 = 0 + 50 Combine like terms: 0 + 50 = 50 9w + w2 = 50 The w term is 9w. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9w + 20.25 + w2 = 50 + 20.25 Reorder the terms: 20.25 + 9w + w2 = 50 + 20.25 Combine like terms: 50 + 20.25 = 70.25 20.25 + 9w + w2 = 70.25 Factor a perfect square on the left side: (w + 4.5)(w + 4.5) = 70.25 Calculate the square root of the right side: 8.381527307 Break this problem into two subproblems by setting (w + 4.5) equal to 8.381527307 and -8.381527307.Subproblem 1
w + 4.5 = 8.381527307 Simplifying w + 4.5 = 8.381527307 Reorder the terms: 4.5 + w = 8.381527307 Solving 4.5 + w = 8.381527307 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + w = 8.381527307 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + w = 8.381527307 + -4.5 w = 8.381527307 + -4.5 Combine like terms: 8.381527307 + -4.5 = 3.881527307 w = 3.881527307 Simplifying w = 3.881527307Subproblem 2
w + 4.5 = -8.381527307 Simplifying w + 4.5 = -8.381527307 Reorder the terms: 4.5 + w = -8.381527307 Solving 4.5 + w = -8.381527307 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + w = -8.381527307 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + w = -8.381527307 + -4.5 w = -8.381527307 + -4.5 Combine like terms: -8.381527307 + -4.5 = -12.881527307 w = -12.881527307 Simplifying w = -12.881527307Solution
The solution to the problem is based on the solutions from the subproblems. w = {3.881527307, -12.881527307}Solution
w = {3.881527307, -12.881527307}
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