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Simplifying (w + 3)(w + 5) = 9 Reorder the terms: (3 + w)(w + 5) = 9 Reorder the terms: (3 + w)(5 + w) = 9 Multiply (3 + w) * (5 + w) (3(5 + w) + w(5 + w)) = 9 ((5 * 3 + w * 3) + w(5 + w)) = 9 ((15 + 3w) + w(5 + w)) = 9 (15 + 3w + (5 * w + w * w)) = 9 (15 + 3w + (5w + w2)) = 9 Combine like terms: 3w + 5w = 8w (15 + 8w + w2) = 9 Solving 15 + 8w + w2 = 9 Solving for variable 'w'. Reorder the terms: 15 + -9 + 8w + w2 = 9 + -9 Combine like terms: 15 + -9 = 6 6 + 8w + w2 = 9 + -9 Combine like terms: 9 + -9 = 0 6 + 8w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + 8w + -6 + w2 = 0 + -6 Reorder the terms: 6 + -6 + 8w + w2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 8w + w2 = 0 + -6 8w + w2 = 0 + -6 Combine like terms: 0 + -6 = -6 8w + w2 = -6 The w term is 8w. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8w + 16 + w2 = -6 + 16 Reorder the terms: 16 + 8w + w2 = -6 + 16 Combine like terms: -6 + 16 = 10 16 + 8w + w2 = 10 Factor a perfect square on the left side: (w + 4)(w + 4) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (w + 4) equal to 3.16227766 and -3.16227766.Subproblem 1
w + 4 = 3.16227766 Simplifying w + 4 = 3.16227766 Reorder the terms: 4 + w = 3.16227766 Solving 4 + w = 3.16227766 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + w = 3.16227766 + -4 Combine like terms: 4 + -4 = 0 0 + w = 3.16227766 + -4 w = 3.16227766 + -4 Combine like terms: 3.16227766 + -4 = -0.83772234 w = -0.83772234 Simplifying w = -0.83772234Subproblem 2
w + 4 = -3.16227766 Simplifying w + 4 = -3.16227766 Reorder the terms: 4 + w = -3.16227766 Solving 4 + w = -3.16227766 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + w = -3.16227766 + -4 Combine like terms: 4 + -4 = 0 0 + w = -3.16227766 + -4 w = -3.16227766 + -4 Combine like terms: -3.16227766 + -4 = -7.16227766 w = -7.16227766 Simplifying w = -7.16227766Solution
The solution to the problem is based on the solutions from the subproblems. w = {-0.83772234, -7.16227766}
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