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Simplifying 0 = -4w2 + 40w + -33 Reorder the terms: 0 = -33 + 40w + -4w2 Solving 0 = -33 + 40w + -4w2 Solving for variable 'w'. Combine like terms: 0 + 33 = 33 33 + -40w + 4w2 = -33 + 40w + -4w2 + 33 + -40w + 4w2 Reorder the terms: 33 + -40w + 4w2 = -33 + 33 + 40w + -40w + -4w2 + 4w2 Combine like terms: -33 + 33 = 0 33 + -40w + 4w2 = 0 + 40w + -40w + -4w2 + 4w2 33 + -40w + 4w2 = 40w + -40w + -4w2 + 4w2 Combine like terms: 40w + -40w = 0 33 + -40w + 4w2 = 0 + -4w2 + 4w2 33 + -40w + 4w2 = -4w2 + 4w2 Combine like terms: -4w2 + 4w2 = 0 33 + -40w + 4w2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 8.25 + -10w + w2 = 0 Move the constant term to the right: Add '-8.25' to each side of the equation. 8.25 + -10w + -8.25 + w2 = 0 + -8.25 Reorder the terms: 8.25 + -8.25 + -10w + w2 = 0 + -8.25 Combine like terms: 8.25 + -8.25 = 0.00 0.00 + -10w + w2 = 0 + -8.25 -10w + w2 = 0 + -8.25 Combine like terms: 0 + -8.25 = -8.25 -10w + w2 = -8.25 The w term is -10w. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10w + 25 + w2 = -8.25 + 25 Reorder the terms: 25 + -10w + w2 = -8.25 + 25 Combine like terms: -8.25 + 25 = 16.75 25 + -10w + w2 = 16.75 Factor a perfect square on the left side: (w + -5)(w + -5) = 16.75 Calculate the square root of the right side: 4.092676386 Break this problem into two subproblems by setting (w + -5) equal to 4.092676386 and -4.092676386.Subproblem 1
w + -5 = 4.092676386 Simplifying w + -5 = 4.092676386 Reorder the terms: -5 + w = 4.092676386 Solving -5 + w = 4.092676386 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + w = 4.092676386 + 5 Combine like terms: -5 + 5 = 0 0 + w = 4.092676386 + 5 w = 4.092676386 + 5 Combine like terms: 4.092676386 + 5 = 9.092676386 w = 9.092676386 Simplifying w = 9.092676386Subproblem 2
w + -5 = -4.092676386 Simplifying w + -5 = -4.092676386 Reorder the terms: -5 + w = -4.092676386 Solving -5 + w = -4.092676386 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + w = -4.092676386 + 5 Combine like terms: -5 + 5 = 0 0 + w = -4.092676386 + 5 w = -4.092676386 + 5 Combine like terms: -4.092676386 + 5 = 0.907323614 w = 0.907323614 Simplifying w = 0.907323614Solution
The solution to the problem is based on the solutions from the subproblems. w = {9.092676386, 0.907323614}
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