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Simplifying w(w + 6) = 36 Reorder the terms: w(6 + w) = 36 (6 * w + w * w) = 36 (6w + w2) = 36 Solving 6w + w2 = 36 Solving for variable 'w'. Reorder the terms: -36 + 6w + w2 = 36 + -36 Combine like terms: 36 + -36 = 0 -36 + 6w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + 6w + 36 + w2 = 0 + 36 Reorder the terms: -36 + 36 + 6w + w2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + 6w + w2 = 0 + 36 6w + w2 = 0 + 36 Combine like terms: 0 + 36 = 36 6w + w2 = 36 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 = 36 + 9 Reorder the terms: 9 + 6w + w2 = 36 + 9 Combine like terms: 36 + 9 = 45 9 + 6w + w2 = 45 Factor a perfect square on the left side: (w + 3)(w + 3) = 45 Calculate the square root of the right side: 6.708203933 Break this problem into two subproblems by setting (w + 3) equal to 6.708203933 and -6.708203933.Subproblem 1
w + 3 = 6.708203933 Simplifying w + 3 = 6.708203933 Reorder the terms: 3 + w = 6.708203933 Solving 3 + w = 6.708203933 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 = 6.708203933 + -3 Combine like terms: 3 + -3 = 0 0 + w = 6.708203933 + -3 w = 6.708203933 + -3 Combine like terms: 6.708203933 + -3 = 3.708203933 w = 3.708203933 Simplifying w = 3.708203933Subproblem 2
w + 3 = -6.708203933 Simplifying w + 3 = -6.708203933 Reorder the terms: 3 + w = -6.708203933 Solving 3 + w = -6.708203933 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 = -6.708203933 + -3 Combine like terms: 3 + -3 = 0 0 + w = -6.708203933 + -3 w = -6.708203933 + -3 Combine like terms: -6.708203933 + -3 = -9.708203933 w = -9.708203933 Simplifying w = -9.708203933Solution
The solution to the problem is based on the solutions from the subproblems. w = {3.708203933, -9.708203933}
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