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Simplifying 9w2 + 9w = 81 Reorder the terms: 9w + 9w2 = 81 Solving 9w + 9w2 = 81 Solving for variable 'w'. Reorder the terms: -81 + 9w + 9w2 = 81 + -81 Combine like terms: 81 + -81 = 0 -81 + 9w + 9w2 = 0 Factor out the Greatest Common Factor (GCF), '9'. 9(-9 + w + w2) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(-9 + w + w2)' equal to zero and attempt to solve: Simplifying -9 + w + w2 = 0 Solving -9 + w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + w + 9 + w2 = 0 + 9 Reorder the terms: -9 + 9 + w + w2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + w + w2 = 0 + 9 w + w2 = 0 + 9 Combine like terms: 0 + 9 = 9 w + w2 = 9 The w term is w. 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. w + 0.25 + w2 = 9 + 0.25 Reorder the terms: 0.25 + w + w2 = 9 + 0.25 Combine like terms: 9 + 0.25 = 9.25 0.25 + w + 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 = 2.541381265 w = 2.541381265 Simplifying w = 2.541381265Subproblem 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 = -3.541381265 w = -3.541381265 Simplifying w = -3.541381265Solution
The solution to the problem is based on the solutions from the subproblems. w = {2.541381265, -3.541381265}Solution
w = {2.541381265, -3.541381265}
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