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Simplifying 72 = (w + 3)(w + 3) Reorder the terms: 72 = (3 + w)(w + 3) Reorder the terms: 72 = (3 + w)(3 + w) Multiply (3 + w) * (3 + w) 72 = (3(3 + w) + w(3 + w)) 72 = ((3 * 3 + w * 3) + w(3 + w)) 72 = ((9 + 3w) + w(3 + w)) 72 = (9 + 3w + (3 * w + w * w)) 72 = (9 + 3w + (3w + w2)) Combine like terms: 3w + 3w = 6w 72 = (9 + 6w + w2) Solving 72 = 9 + 6w + w2 Solving for variable 'w'. Combine like terms: 72 + -9 = 63 63 + -6w + -1w2 = 9 + 6w + w2 + -9 + -6w + -1w2 Reorder the terms: 63 + -6w + -1w2 = 9 + -9 + 6w + -6w + w2 + -1w2 Combine like terms: 9 + -9 = 0 63 + -6w + -1w2 = 0 + 6w + -6w + w2 + -1w2 63 + -6w + -1w2 = 6w + -6w + w2 + -1w2 Combine like terms: 6w + -6w = 0 63 + -6w + -1w2 = 0 + w2 + -1w2 63 + -6w + -1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 63 + -6w + -1w2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -63 + 6w + w2 = 0 Move the constant term to the right: Add '63' to each side of the equation. -63 + 6w + 63 + w2 = 0 + 63 Reorder the terms: -63 + 63 + 6w + w2 = 0 + 63 Combine like terms: -63 + 63 = 0 0 + 6w + w2 = 0 + 63 6w + w2 = 0 + 63 Combine like terms: 0 + 63 = 63 6w + w2 = 63 The w term is 6w. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6w + 9 + w2 = 63 + 9 Reorder the terms: 9 + 6w + w2 = 63 + 9 Combine like terms: 63 + 9 = 72 9 + 6w + w2 = 72 Factor a perfect square on the left side: (w + 3)(w + 3) = 72 Calculate the square root of the right side: 8.485281374 Break this problem into two subproblems by setting (w + 3) equal to 8.485281374 and -8.485281374.Subproblem 1
w + 3 = 8.485281374 Simplifying w + 3 = 8.485281374 Reorder the terms: 3 + w = 8.485281374 Solving 3 + w = 8.485281374 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + w = 8.485281374 + -3 Combine like terms: 3 + -3 = 0 0 + w = 8.485281374 + -3 w = 8.485281374 + -3 Combine like terms: 8.485281374 + -3 = 5.485281374 w = 5.485281374 Simplifying w = 5.485281374Subproblem 2
w + 3 = -8.485281374 Simplifying w + 3 = -8.485281374 Reorder the terms: 3 + w = -8.485281374 Solving 3 + w = -8.485281374 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + w = -8.485281374 + -3 Combine like terms: 3 + -3 = 0 0 + w = -8.485281374 + -3 w = -8.485281374 + -3 Combine like terms: -8.485281374 + -3 = -11.485281374 w = -11.485281374 Simplifying w = -11.485281374Solution
The solution to the problem is based on the solutions from the subproblems. w = {5.485281374, -11.485281374}
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