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Simplifying (w + -9)(w + -9) = 12 Reorder the terms: (-9 + w)(w + -9) = 12 Reorder the terms: (-9 + w)(-9 + w) = 12 Multiply (-9 + w) * (-9 + w) (-9(-9 + w) + w(-9 + w)) = 12 ((-9 * -9 + w * -9) + w(-9 + w)) = 12 ((81 + -9w) + w(-9 + w)) = 12 (81 + -9w + (-9 * w + w * w)) = 12 (81 + -9w + (-9w + w2)) = 12 Combine like terms: -9w + -9w = -18w (81 + -18w + w2) = 12 Solving 81 + -18w + w2 = 12 Solving for variable 'w'. Reorder the terms: 81 + -12 + -18w + w2 = 12 + -12 Combine like terms: 81 + -12 = 69 69 + -18w + w2 = 12 + -12 Combine like terms: 12 + -12 = 0 69 + -18w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '-69' to each side of the equation. 69 + -18w + -69 + w2 = 0 + -69 Reorder the terms: 69 + -69 + -18w + w2 = 0 + -69 Combine like terms: 69 + -69 = 0 0 + -18w + w2 = 0 + -69 -18w + w2 = 0 + -69 Combine like terms: 0 + -69 = -69 -18w + w2 = -69 The w term is -18w. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18w + 81 + w2 = -69 + 81 Reorder the terms: 81 + -18w + w2 = -69 + 81 Combine like terms: -69 + 81 = 12 81 + -18w + w2 = 12 Factor a perfect square on the left side: (w + -9)(w + -9) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (w + -9) equal to 3.464101615 and -3.464101615.Subproblem 1
w + -9 = 3.464101615 Simplifying w + -9 = 3.464101615 Reorder the terms: -9 + w = 3.464101615 Solving -9 + w = 3.464101615 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + w = 3.464101615 + 9 Combine like terms: -9 + 9 = 0 0 + w = 3.464101615 + 9 w = 3.464101615 + 9 Combine like terms: 3.464101615 + 9 = 12.464101615 w = 12.464101615 Simplifying w = 12.464101615Subproblem 2
w + -9 = -3.464101615 Simplifying w + -9 = -3.464101615 Reorder the terms: -9 + w = -3.464101615 Solving -9 + w = -3.464101615 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + w = -3.464101615 + 9 Combine like terms: -9 + 9 = 0 0 + w = -3.464101615 + 9 w = -3.464101615 + 9 Combine like terms: -3.464101615 + 9 = 5.535898385 w = 5.535898385 Simplifying w = 5.535898385Solution
The solution to the problem is based on the solutions from the subproblems. w = {12.464101615, 5.535898385}
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