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Simplifying (w + -3)(w + 3) = 9 + 2w Reorder the terms: (-3 + w)(w + 3) = 9 + 2w Reorder the terms: (-3 + w)(3 + w) = 9 + 2w Multiply (-3 + w) * (3 + w) (-3(3 + w) + w(3 + w)) = 9 + 2w ((3 * -3 + w * -3) + w(3 + w)) = 9 + 2w ((-9 + -3w) + w(3 + w)) = 9 + 2w (-9 + -3w + (3 * w + w * w)) = 9 + 2w (-9 + -3w + (3w + w2)) = 9 + 2w Combine like terms: -3w + 3w = 0 (-9 + 0 + w2) = 9 + 2w (-9 + w2) = 9 + 2w Solving -9 + w2 = 9 + 2w Solving for variable 'w'. Reorder the terms: -9 + -9 + -2w + w2 = 9 + 2w + -9 + -2w Combine like terms: -9 + -9 = -18 -18 + -2w + w2 = 9 + 2w + -9 + -2w Reorder the terms: -18 + -2w + w2 = 9 + -9 + 2w + -2w Combine like terms: 9 + -9 = 0 -18 + -2w + w2 = 0 + 2w + -2w -18 + -2w + w2 = 2w + -2w Combine like terms: 2w + -2w = 0 -18 + -2w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + -2w + 18 + w2 = 0 + 18 Reorder the terms: -18 + 18 + -2w + w2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -2w + w2 = 0 + 18 -2w + w2 = 0 + 18 Combine like terms: 0 + 18 = 18 -2w + w2 = 18 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 = 18 + 1 Reorder the terms: 1 + -2w + w2 = 18 + 1 Combine like terms: 18 + 1 = 19 1 + -2w + w2 = 19 Factor a perfect square on the left side: (w + -1)(w + -1) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (w + -1) equal to 4.358898944 and -4.358898944.Subproblem 1
w + -1 = 4.358898944 Simplifying w + -1 = 4.358898944 Reorder the terms: -1 + w = 4.358898944 Solving -1 + w = 4.358898944 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 = 4.358898944 + 1 Combine like terms: -1 + 1 = 0 0 + w = 4.358898944 + 1 w = 4.358898944 + 1 Combine like terms: 4.358898944 + 1 = 5.358898944 w = 5.358898944 Simplifying w = 5.358898944Subproblem 2
w + -1 = -4.358898944 Simplifying w + -1 = -4.358898944 Reorder the terms: -1 + w = -4.358898944 Solving -1 + w = -4.358898944 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 = -4.358898944 + 1 Combine like terms: -1 + 1 = 0 0 + w = -4.358898944 + 1 w = -4.358898944 + 1 Combine like terms: -4.358898944 + 1 = -3.358898944 w = -3.358898944 Simplifying w = -3.358898944Solution
The solution to the problem is based on the solutions from the subproblems. w = {5.358898944, -3.358898944}
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