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Simplifying 2(w2 + -1w + -36) = 0 Reorder the terms: 2(-36 + -1w + w2) = 0 (-36 * 2 + -1w * 2 + w2 * 2) = 0 (-72 + -2w + 2w2) = 0 Solving -72 + -2w + 2w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2'. 2(-36 + -1w + w2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-36 + -1w + w2)' equal to zero and attempt to solve: Simplifying -36 + -1w + w2 = 0 Solving -36 + -1w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + -1w + 36 + w2 = 0 + 36 Reorder the terms: -36 + 36 + -1w + w2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -1w + w2 = 0 + 36 -1w + w2 = 0 + 36 Combine like terms: 0 + 36 = 36 -1w + w2 = 36 The w term is -1w. 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. -1w + 0.25 + w2 = 36 + 0.25 Reorder the terms: 0.25 + -1w + w2 = 36 + 0.25 Combine like terms: 36 + 0.25 = 36.25 0.25 + -1w + w2 = 36.25 Factor a perfect square on the left side: (w + -0.5)(w + -0.5) = 36.25 Calculate the square root of the right side: 6.020797289 Break this problem into two subproblems by setting (w + -0.5) equal to 6.020797289 and -6.020797289.Subproblem 1
w + -0.5 = 6.020797289 Simplifying w + -0.5 = 6.020797289 Reorder the terms: -0.5 + w = 6.020797289 Solving -0.5 + w = 6.020797289 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 = 6.020797289 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + w = 6.020797289 + 0.5 w = 6.020797289 + 0.5 Combine like terms: 6.020797289 + 0.5 = 6.520797289 w = 6.520797289 Simplifying w = 6.520797289Subproblem 2
w + -0.5 = -6.020797289 Simplifying w + -0.5 = -6.020797289 Reorder the terms: -0.5 + w = -6.020797289 Solving -0.5 + w = -6.020797289 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 = -6.020797289 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + w = -6.020797289 + 0.5 w = -6.020797289 + 0.5 Combine like terms: -6.020797289 + 0.5 = -5.520797289 w = -5.520797289 Simplifying w = -5.520797289Solution
The solution to the problem is based on the solutions from the subproblems. w = {6.520797289, -5.520797289}Solution
w = {6.520797289, -5.520797289}
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