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Simplifying 2(W + 7)(W + -3) = W2 + 7W + 114 Reorder the terms: 2(7 + W)(W + -3) = W2 + 7W + 114 Reorder the terms: 2(7 + W)(-3 + W) = W2 + 7W + 114 Multiply (7 + W) * (-3 + W) 2(7(-3 + W) + W(-3 + W)) = W2 + 7W + 114 2((-3 * 7 + W * 7) + W(-3 + W)) = W2 + 7W + 114 2((-21 + 7W) + W(-3 + W)) = W2 + 7W + 114 2(-21 + 7W + (-3 * W + W * W)) = W2 + 7W + 114 2(-21 + 7W + (-3W + W2)) = W2 + 7W + 114 Combine like terms: 7W + -3W = 4W 2(-21 + 4W + W2) = W2 + 7W + 114 (-21 * 2 + 4W * 2 + W2 * 2) = W2 + 7W + 114 (-42 + 8W + 2W2) = W2 + 7W + 114 Reorder the terms: -42 + 8W + 2W2 = 114 + 7W + W2 Solving -42 + 8W + 2W2 = 114 + 7W + W2 Solving for variable 'W'. Reorder the terms: -42 + -114 + 8W + -7W + 2W2 + -1W2 = 114 + 7W + W2 + -114 + -7W + -1W2 Combine like terms: -42 + -114 = -156 -156 + 8W + -7W + 2W2 + -1W2 = 114 + 7W + W2 + -114 + -7W + -1W2 Combine like terms: 8W + -7W = 1W -156 + 1W + 2W2 + -1W2 = 114 + 7W + W2 + -114 + -7W + -1W2 Combine like terms: 2W2 + -1W2 = 1W2 -156 + 1W + 1W2 = 114 + 7W + W2 + -114 + -7W + -1W2 Reorder the terms: -156 + 1W + 1W2 = 114 + -114 + 7W + -7W + W2 + -1W2 Combine like terms: 114 + -114 = 0 -156 + 1W + 1W2 = 0 + 7W + -7W + W2 + -1W2 -156 + 1W + 1W2 = 7W + -7W + W2 + -1W2 Combine like terms: 7W + -7W = 0 -156 + 1W + 1W2 = 0 + W2 + -1W2 -156 + 1W + 1W2 = W2 + -1W2 Combine like terms: W2 + -1W2 = 0 -156 + 1W + 1W2 = 0 Factor a trinomial. (-13 + -1W)(12 + -1W) = 0Subproblem 1
Set the factor '(-13 + -1W)' equal to zero and attempt to solve: Simplifying -13 + -1W = 0 Solving -13 + -1W = 0 Move all terms containing W to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + -1W = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -1W = 0 + 13 -1W = 0 + 13 Combine like terms: 0 + 13 = 13 -1W = 13 Divide each side by '-1'. W = -13 Simplifying W = -13Subproblem 2
Set the factor '(12 + -1W)' equal to zero and attempt to solve: Simplifying 12 + -1W = 0 Solving 12 + -1W = 0 Move all terms containing W to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1W = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1W = 0 + -12 -1W = 0 + -12 Combine like terms: 0 + -12 = -12 -1W = -12 Divide each side by '-1'. W = 12 Simplifying W = 12Solution
W = {-13, 12}
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