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Simplifying (w + 3)(w + 3) = 2w2 + -10w + -12 Reorder the terms: (3 + w)(w + 3) = 2w2 + -10w + -12 Reorder the terms: (3 + w)(3 + w) = 2w2 + -10w + -12 Multiply (3 + w) * (3 + w) (3(3 + w) + w(3 + w)) = 2w2 + -10w + -12 ((3 * 3 + w * 3) + w(3 + w)) = 2w2 + -10w + -12 ((9 + 3w) + w(3 + w)) = 2w2 + -10w + -12 (9 + 3w + (3 * w + w * w)) = 2w2 + -10w + -12 (9 + 3w + (3w + w2)) = 2w2 + -10w + -12 Combine like terms: 3w + 3w = 6w (9 + 6w + w2) = 2w2 + -10w + -12 Reorder the terms: 9 + 6w + w2 = -12 + -10w + 2w2 Solving 9 + 6w + w2 = -12 + -10w + 2w2 Solving for variable 'w'. Reorder the terms: 9 + 12 + 6w + 10w + w2 + -2w2 = -12 + -10w + 2w2 + 12 + 10w + -2w2 Combine like terms: 9 + 12 = 21 21 + 6w + 10w + w2 + -2w2 = -12 + -10w + 2w2 + 12 + 10w + -2w2 Combine like terms: 6w + 10w = 16w 21 + 16w + w2 + -2w2 = -12 + -10w + 2w2 + 12 + 10w + -2w2 Combine like terms: w2 + -2w2 = -1w2 21 + 16w + -1w2 = -12 + -10w + 2w2 + 12 + 10w + -2w2 Reorder the terms: 21 + 16w + -1w2 = -12 + 12 + -10w + 10w + 2w2 + -2w2 Combine like terms: -12 + 12 = 0 21 + 16w + -1w2 = 0 + -10w + 10w + 2w2 + -2w2 21 + 16w + -1w2 = -10w + 10w + 2w2 + -2w2 Combine like terms: -10w + 10w = 0 21 + 16w + -1w2 = 0 + 2w2 + -2w2 21 + 16w + -1w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 21 + 16w + -1w2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -21 + -16w + w2 = 0 Move the constant term to the right: Add '21' to each side of the equation. -21 + -16w + 21 + w2 = 0 + 21 Reorder the terms: -21 + 21 + -16w + w2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -16w + w2 = 0 + 21 -16w + w2 = 0 + 21 Combine like terms: 0 + 21 = 21 -16w + w2 = 21 The w term is -16w. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16w + 64 + w2 = 21 + 64 Reorder the terms: 64 + -16w + w2 = 21 + 64 Combine like terms: 21 + 64 = 85 64 + -16w + w2 = 85 Factor a perfect square on the left side: (w + -8)(w + -8) = 85 Calculate the square root of the right side: 9.219544457 Break this problem into two subproblems by setting (w + -8) equal to 9.219544457 and -9.219544457.Subproblem 1
w + -8 = 9.219544457 Simplifying w + -8 = 9.219544457 Reorder the terms: -8 + w = 9.219544457 Solving -8 + w = 9.219544457 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + w = 9.219544457 + 8 Combine like terms: -8 + 8 = 0 0 + w = 9.219544457 + 8 w = 9.219544457 + 8 Combine like terms: 9.219544457 + 8 = 17.219544457 w = 17.219544457 Simplifying w = 17.219544457Subproblem 2
w + -8 = -9.219544457 Simplifying w + -8 = -9.219544457 Reorder the terms: -8 + w = -9.219544457 Solving -8 + w = -9.219544457 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + w = -9.219544457 + 8 Combine like terms: -8 + 8 = 0 0 + w = -9.219544457 + 8 w = -9.219544457 + 8 Combine like terms: -9.219544457 + 8 = -1.219544457 w = -1.219544457 Simplifying w = -1.219544457Solution
The solution to the problem is based on the solutions from the subproblems. w = {17.219544457, -1.219544457}
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