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Simplifying w2 + -4w + -72 = 0 Reorder the terms: -72 + -4w + w2 = 0 Solving -72 + -4w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '72' to each side of the equation. -72 + -4w + 72 + w2 = 0 + 72 Reorder the terms: -72 + 72 + -4w + w2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + -4w + w2 = 0 + 72 -4w + w2 = 0 + 72 Combine like terms: 0 + 72 = 72 -4w + w2 = 72 The w term is -4w. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4w + 4 + w2 = 72 + 4 Reorder the terms: 4 + -4w + w2 = 72 + 4 Combine like terms: 72 + 4 = 76 4 + -4w + w2 = 76 Factor a perfect square on the left side: (w + -2)(w + -2) = 76 Calculate the square root of the right side: 8.717797887 Break this problem into two subproblems by setting (w + -2) equal to 8.717797887 and -8.717797887.Subproblem 1
w + -2 = 8.717797887 Simplifying w + -2 = 8.717797887 Reorder the terms: -2 + w = 8.717797887 Solving -2 + w = 8.717797887 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + w = 8.717797887 + 2 Combine like terms: -2 + 2 = 0 0 + w = 8.717797887 + 2 w = 8.717797887 + 2 Combine like terms: 8.717797887 + 2 = 10.717797887 w = 10.717797887 Simplifying w = 10.717797887Subproblem 2
w + -2 = -8.717797887 Simplifying w + -2 = -8.717797887 Reorder the terms: -2 + w = -8.717797887 Solving -2 + w = -8.717797887 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + w = -8.717797887 + 2 Combine like terms: -2 + 2 = 0 0 + w = -8.717797887 + 2 w = -8.717797887 + 2 Combine like terms: -8.717797887 + 2 = -6.717797887 w = -6.717797887 Simplifying w = -6.717797887Solution
The solution to the problem is based on the solutions from the subproblems. w = {10.717797887, -6.717797887}
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