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Simplifying 0 = 3w2 + -7w + -88 Reorder the terms: 0 = -88 + -7w + 3w2 Solving 0 = -88 + -7w + 3w2 Solving for variable 'w'. Combine like terms: 0 + 88 = 88 88 + 7w + -3w2 = -88 + -7w + 3w2 + 88 + 7w + -3w2 Reorder the terms: 88 + 7w + -3w2 = -88 + 88 + -7w + 7w + 3w2 + -3w2 Combine like terms: -88 + 88 = 0 88 + 7w + -3w2 = 0 + -7w + 7w + 3w2 + -3w2 88 + 7w + -3w2 = -7w + 7w + 3w2 + -3w2 Combine like terms: -7w + 7w = 0 88 + 7w + -3w2 = 0 + 3w2 + -3w2 88 + 7w + -3w2 = 3w2 + -3w2 Combine like terms: 3w2 + -3w2 = 0 88 + 7w + -3w2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -29.33333333 + -2.333333333w + w2 = 0 Move the constant term to the right: Add '29.33333333' to each side of the equation. -29.33333333 + -2.333333333w + 29.33333333 + w2 = 0 + 29.33333333 Reorder the terms: -29.33333333 + 29.33333333 + -2.333333333w + w2 = 0 + 29.33333333 Combine like terms: -29.33333333 + 29.33333333 = 0.00000000 0.00000000 + -2.333333333w + w2 = 0 + 29.33333333 -2.333333333w + w2 = 0 + 29.33333333 Combine like terms: 0 + 29.33333333 = 29.33333333 -2.333333333w + w2 = 29.33333333 The w term is -2.333333333w. Take half its coefficient (-1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. -2.333333333w + 1.361111112 + w2 = 29.33333333 + 1.361111112 Reorder the terms: 1.361111112 + -2.333333333w + w2 = 29.33333333 + 1.361111112 Combine like terms: 29.33333333 + 1.361111112 = 30.694444442 1.361111112 + -2.333333333w + w2 = 30.694444442 Factor a perfect square on the left side: (w + -1.166666667)(w + -1.166666667) = 30.694444442 Calculate the square root of the right side: 5.540256713 Break this problem into two subproblems by setting (w + -1.166666667) equal to 5.540256713 and -5.540256713.Subproblem 1
w + -1.166666667 = 5.540256713 Simplifying w + -1.166666667 = 5.540256713 Reorder the terms: -1.166666667 + w = 5.540256713 Solving -1.166666667 + w = 5.540256713 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + w = 5.540256713 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + w = 5.540256713 + 1.166666667 w = 5.540256713 + 1.166666667 Combine like terms: 5.540256713 + 1.166666667 = 6.70692338 w = 6.70692338 Simplifying w = 6.70692338Subproblem 2
w + -1.166666667 = -5.540256713 Simplifying w + -1.166666667 = -5.540256713 Reorder the terms: -1.166666667 + w = -5.540256713 Solving -1.166666667 + w = -5.540256713 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + w = -5.540256713 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + w = -5.540256713 + 1.166666667 w = -5.540256713 + 1.166666667 Combine like terms: -5.540256713 + 1.166666667 = -4.373590046 w = -4.373590046 Simplifying w = -4.373590046Solution
The solution to the problem is based on the solutions from the subproblems. w = {6.70692338, -4.373590046}
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