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Simplifying -1w2 + 33w + -66 = 0 Reorder the terms: -66 + 33w + -1w2 = 0 Solving -66 + 33w + -1w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 66 + -33w + w2 = 0 Move the constant term to the right: Add '-66' to each side of the equation. 66 + -33w + -66 + w2 = 0 + -66 Reorder the terms: 66 + -66 + -33w + w2 = 0 + -66 Combine like terms: 66 + -66 = 0 0 + -33w + w2 = 0 + -66 -33w + w2 = 0 + -66 Combine like terms: 0 + -66 = -66 -33w + w2 = -66 The w term is -33w. Take half its coefficient (-16.5). Square it (272.25) and add it to both sides. Add '272.25' to each side of the equation. -33w + 272.25 + w2 = -66 + 272.25 Reorder the terms: 272.25 + -33w + w2 = -66 + 272.25 Combine like terms: -66 + 272.25 = 206.25 272.25 + -33w + w2 = 206.25 Factor a perfect square on the left side: (w + -16.5)(w + -16.5) = 206.25 Calculate the square root of the right side: 14.361406616 Break this problem into two subproblems by setting (w + -16.5) equal to 14.361406616 and -14.361406616.Subproblem 1
w + -16.5 = 14.361406616 Simplifying w + -16.5 = 14.361406616 Reorder the terms: -16.5 + w = 14.361406616 Solving -16.5 + w = 14.361406616 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '16.5' to each side of the equation. -16.5 + 16.5 + w = 14.361406616 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + w = 14.361406616 + 16.5 w = 14.361406616 + 16.5 Combine like terms: 14.361406616 + 16.5 = 30.861406616 w = 30.861406616 Simplifying w = 30.861406616Subproblem 2
w + -16.5 = -14.361406616 Simplifying w + -16.5 = -14.361406616 Reorder the terms: -16.5 + w = -14.361406616 Solving -16.5 + w = -14.361406616 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '16.5' to each side of the equation. -16.5 + 16.5 + w = -14.361406616 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + w = -14.361406616 + 16.5 w = -14.361406616 + 16.5 Combine like terms: -14.361406616 + 16.5 = 2.138593384 w = 2.138593384 Simplifying w = 2.138593384Solution
The solution to the problem is based on the solutions from the subproblems. w = {30.861406616, 2.138593384}
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