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Simplifying 64 = w(w + -4) Reorder the terms: 64 = w(-4 + w) 64 = (-4 * w + w * w) 64 = (-4w + w2) Solving 64 = -4w + w2 Solving for variable 'w'. Reorder the terms: 64 + 4w + -1w2 = -4w + 4w + w2 + -1w2 Combine like terms: -4w + 4w = 0 64 + 4w + -1w2 = 0 + w2 + -1w2 64 + 4w + -1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 64 + 4w + -1w2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -64 + -4w + w2 = 0 Move the constant term to the right: Add '64' to each side of the equation. -64 + -4w + 64 + w2 = 0 + 64 Reorder the terms: -64 + 64 + -4w + w2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + -4w + w2 = 0 + 64 -4w + w2 = 0 + 64 Combine like terms: 0 + 64 = 64 -4w + w2 = 64 The w term is -4w. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4w + 4 + w2 = 64 + 4 Reorder the terms: 4 + -4w + w2 = 64 + 4 Combine like terms: 64 + 4 = 68 4 + -4w + w2 = 68 Factor a perfect square on the left side: (w + -2)(w + -2) = 68 Calculate the square root of the right side: 8.246211251 Break this problem into two subproblems by setting (w + -2) equal to 8.246211251 and -8.246211251.Subproblem 1
w + -2 = 8.246211251 Simplifying w + -2 = 8.246211251 Reorder the terms: -2 + w = 8.246211251 Solving -2 + w = 8.246211251 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + w = 8.246211251 + 2 Combine like terms: -2 + 2 = 0 0 + w = 8.246211251 + 2 w = 8.246211251 + 2 Combine like terms: 8.246211251 + 2 = 10.246211251 w = 10.246211251 Simplifying w = 10.246211251Subproblem 2
w + -2 = -8.246211251 Simplifying w + -2 = -8.246211251 Reorder the terms: -2 + w = -8.246211251 Solving -2 + w = -8.246211251 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + w = -8.246211251 + 2 Combine like terms: -2 + 2 = 0 0 + w = -8.246211251 + 2 w = -8.246211251 + 2 Combine like terms: -8.246211251 + 2 = -6.246211251 w = -6.246211251 Simplifying w = -6.246211251Solution
The solution to the problem is based on the solutions from the subproblems. w = {10.246211251, -6.246211251}
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