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Simplifying w2 + -9w + -16 = 0 Reorder the terms: -16 + -9w + w2 = 0 Solving -16 + -9w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + -9w + 16 + w2 = 0 + 16 Reorder the terms: -16 + 16 + -9w + w2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -9w + w2 = 0 + 16 -9w + w2 = 0 + 16 Combine like terms: 0 + 16 = 16 -9w + w2 = 16 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 = 16 + 20.25 Reorder the terms: 20.25 + -9w + w2 = 16 + 20.25 Combine like terms: 16 + 20.25 = 36.25 20.25 + -9w + w2 = 36.25 Factor a perfect square on the left side: (w + -4.5)(w + -4.5) = 36.25 Calculate the square root of the right side: 6.020797289 Break this problem into two subproblems by setting (w + -4.5) equal to 6.020797289 and -6.020797289.Subproblem 1
w + -4.5 = 6.020797289 Simplifying w + -4.5 = 6.020797289 Reorder the terms: -4.5 + w = 6.020797289 Solving -4.5 + w = 6.020797289 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 = 6.020797289 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + w = 6.020797289 + 4.5 w = 6.020797289 + 4.5 Combine like terms: 6.020797289 + 4.5 = 10.520797289 w = 10.520797289 Simplifying w = 10.520797289Subproblem 2
w + -4.5 = -6.020797289 Simplifying w + -4.5 = -6.020797289 Reorder the terms: -4.5 + w = -6.020797289 Solving -4.5 + w = -6.020797289 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 = -6.020797289 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + w = -6.020797289 + 4.5 w = -6.020797289 + 4.5 Combine like terms: -6.020797289 + 4.5 = -1.520797289 w = -1.520797289 Simplifying w = -1.520797289Solution
The solution to the problem is based on the solutions from the subproblems. w = {10.520797289, -1.520797289}
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