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Simplifying w2 + -47w + -90 = 0 Reorder the terms: -90 + -47w + w2 = 0 Solving -90 + -47w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '90' to each side of the equation. -90 + -47w + 90 + w2 = 0 + 90 Reorder the terms: -90 + 90 + -47w + w2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + -47w + w2 = 0 + 90 -47w + w2 = 0 + 90 Combine like terms: 0 + 90 = 90 -47w + w2 = 90 The w term is -47w. Take half its coefficient (-23.5). Square it (552.25) and add it to both sides. Add '552.25' to each side of the equation. -47w + 552.25 + w2 = 90 + 552.25 Reorder the terms: 552.25 + -47w + w2 = 90 + 552.25 Combine like terms: 90 + 552.25 = 642.25 552.25 + -47w + w2 = 642.25 Factor a perfect square on the left side: (w + -23.5)(w + -23.5) = 642.25 Calculate the square root of the right side: 25.342651795 Break this problem into two subproblems by setting (w + -23.5) equal to 25.342651795 and -25.342651795.Subproblem 1
w + -23.5 = 25.342651795 Simplifying w + -23.5 = 25.342651795 Reorder the terms: -23.5 + w = 25.342651795 Solving -23.5 + w = 25.342651795 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '23.5' to each side of the equation. -23.5 + 23.5 + w = 25.342651795 + 23.5 Combine like terms: -23.5 + 23.5 = 0.0 0.0 + w = 25.342651795 + 23.5 w = 25.342651795 + 23.5 Combine like terms: 25.342651795 + 23.5 = 48.842651795 w = 48.842651795 Simplifying w = 48.842651795Subproblem 2
w + -23.5 = -25.342651795 Simplifying w + -23.5 = -25.342651795 Reorder the terms: -23.5 + w = -25.342651795 Solving -23.5 + w = -25.342651795 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '23.5' to each side of the equation. -23.5 + 23.5 + w = -25.342651795 + 23.5 Combine like terms: -23.5 + 23.5 = 0.0 0.0 + w = -25.342651795 + 23.5 w = -25.342651795 + 23.5 Combine like terms: -25.342651795 + 23.5 = -1.842651795 w = -1.842651795 Simplifying w = -1.842651795Solution
The solution to the problem is based on the solutions from the subproblems. w = {48.842651795, -1.842651795}
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