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Simplifying -1200 + 75w + -1w2 = 0 Solving -1200 + 75w + -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'. 1200 + -75w + w2 = 0 Move the constant term to the right: Add '-1200' to each side of the equation. 1200 + -75w + -1200 + w2 = 0 + -1200 Reorder the terms: 1200 + -1200 + -75w + w2 = 0 + -1200 Combine like terms: 1200 + -1200 = 0 0 + -75w + w2 = 0 + -1200 -75w + w2 = 0 + -1200 Combine like terms: 0 + -1200 = -1200 -75w + w2 = -1200 The w term is -75w. Take half its coefficient (-37.5). Square it (1406.25) and add it to both sides. Add '1406.25' to each side of the equation. -75w + 1406.25 + w2 = -1200 + 1406.25 Reorder the terms: 1406.25 + -75w + w2 = -1200 + 1406.25 Combine like terms: -1200 + 1406.25 = 206.25 1406.25 + -75w + w2 = 206.25 Factor a perfect square on the left side: (w + -37.5)(w + -37.5) = 206.25 Calculate the square root of the right side: 14.361406616 Break this problem into two subproblems by setting (w + -37.5) equal to 14.361406616 and -14.361406616.Subproblem 1
w + -37.5 = 14.361406616 Simplifying w + -37.5 = 14.361406616 Reorder the terms: -37.5 + w = 14.361406616 Solving -37.5 + w = 14.361406616 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '37.5' to each side of the equation. -37.5 + 37.5 + w = 14.361406616 + 37.5 Combine like terms: -37.5 + 37.5 = 0.0 0.0 + w = 14.361406616 + 37.5 w = 14.361406616 + 37.5 Combine like terms: 14.361406616 + 37.5 = 51.861406616 w = 51.861406616 Simplifying w = 51.861406616Subproblem 2
w + -37.5 = -14.361406616 Simplifying w + -37.5 = -14.361406616 Reorder the terms: -37.5 + w = -14.361406616 Solving -37.5 + w = -14.361406616 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '37.5' to each side of the equation. -37.5 + 37.5 + w = -14.361406616 + 37.5 Combine like terms: -37.5 + 37.5 = 0.0 0.0 + w = -14.361406616 + 37.5 w = -14.361406616 + 37.5 Combine like terms: -14.361406616 + 37.5 = 23.138593384 w = 23.138593384 Simplifying w = 23.138593384Solution
The solution to the problem is based on the solutions from the subproblems. w = {51.861406616, 23.138593384}
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