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Simplifying 63 = w(2w + -4) Reorder the terms: 63 = w(-4 + 2w) 63 = (-4 * w + 2w * w) 63 = (-4w + 2w2) Solving 63 = -4w + 2w2 Solving for variable 'w'. Reorder the terms: 63 + 4w + -2w2 = -4w + 4w + 2w2 + -2w2 Combine like terms: -4w + 4w = 0 63 + 4w + -2w2 = 0 + 2w2 + -2w2 63 + 4w + -2w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 63 + 4w + -2w2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -31.5 + -2w + w2 = 0 Move the constant term to the right: Add '31.5' to each side of the equation. -31.5 + -2w + 31.5 + w2 = 0 + 31.5 Reorder the terms: -31.5 + 31.5 + -2w + w2 = 0 + 31.5 Combine like terms: -31.5 + 31.5 = 0.0 0.0 + -2w + w2 = 0 + 31.5 -2w + w2 = 0 + 31.5 Combine like terms: 0 + 31.5 = 31.5 -2w + w2 = 31.5 The w term is -2w. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2w + 1 + w2 = 31.5 + 1 Reorder the terms: 1 + -2w + w2 = 31.5 + 1 Combine like terms: 31.5 + 1 = 32.5 1 + -2w + w2 = 32.5 Factor a perfect square on the left side: (w + -1)(w + -1) = 32.5 Calculate the square root of the right side: 5.700877125 Break this problem into two subproblems by setting (w + -1) equal to 5.700877125 and -5.700877125.Subproblem 1
w + -1 = 5.700877125 Simplifying w + -1 = 5.700877125 Reorder the terms: -1 + w = 5.700877125 Solving -1 + w = 5.700877125 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + w = 5.700877125 + 1 Combine like terms: -1 + 1 = 0 0 + w = 5.700877125 + 1 w = 5.700877125 + 1 Combine like terms: 5.700877125 + 1 = 6.700877125 w = 6.700877125 Simplifying w = 6.700877125Subproblem 2
w + -1 = -5.700877125 Simplifying w + -1 = -5.700877125 Reorder the terms: -1 + w = -5.700877125 Solving -1 + w = -5.700877125 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + w = -5.700877125 + 1 Combine like terms: -1 + 1 = 0 0 + w = -5.700877125 + 1 w = -5.700877125 + 1 Combine like terms: -5.700877125 + 1 = -4.700877125 w = -4.700877125 Simplifying w = -4.700877125Solution
The solution to the problem is based on the solutions from the subproblems. w = {6.700877125, -4.700877125}
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