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Simplifying 36w + -16 + -1w2 = 0 Reorder the terms: -16 + 36w + -1w2 = 0 Solving -16 + 36w + -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'. 16 + -36w + w2 = 0 Move the constant term to the right: Add '-16' to each side of the equation. 16 + -36w + -16 + w2 = 0 + -16 Reorder the terms: 16 + -16 + -36w + w2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -36w + w2 = 0 + -16 -36w + w2 = 0 + -16 Combine like terms: 0 + -16 = -16 -36w + w2 = -16 The w term is -36w. Take half its coefficient (-18). Square it (324) and add it to both sides. Add '324' to each side of the equation. -36w + 324 + w2 = -16 + 324 Reorder the terms: 324 + -36w + w2 = -16 + 324 Combine like terms: -16 + 324 = 308 324 + -36w + w2 = 308 Factor a perfect square on the left side: (w + -18)(w + -18) = 308 Calculate the square root of the right side: 17.549928775 Break this problem into two subproblems by setting (w + -18) equal to 17.549928775 and -17.549928775.Subproblem 1
w + -18 = 17.549928775 Simplifying w + -18 = 17.549928775 Reorder the terms: -18 + w = 17.549928775 Solving -18 + w = 17.549928775 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + w = 17.549928775 + 18 Combine like terms: -18 + 18 = 0 0 + w = 17.549928775 + 18 w = 17.549928775 + 18 Combine like terms: 17.549928775 + 18 = 35.549928775 w = 35.549928775 Simplifying w = 35.549928775Subproblem 2
w + -18 = -17.549928775 Simplifying w + -18 = -17.549928775 Reorder the terms: -18 + w = -17.549928775 Solving -18 + w = -17.549928775 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + w = -17.549928775 + 18 Combine like terms: -18 + 18 = 0 0 + w = -17.549928775 + 18 w = -17.549928775 + 18 Combine like terms: -17.549928775 + 18 = 0.450071225 w = 0.450071225 Simplifying w = 0.450071225Solution
The solution to the problem is based on the solutions from the subproblems. w = {35.549928775, 0.450071225}
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