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Simplifying 150 = 2(3 + w)(w + -1) Reorder the terms: 150 = 2(3 + w)(-1 + w) Multiply (3 + w) * (-1 + w) 150 = 2(3(-1 + w) + w(-1 + w)) 150 = 2((-1 * 3 + w * 3) + w(-1 + w)) 150 = 2((-3 + 3w) + w(-1 + w)) 150 = 2(-3 + 3w + (-1 * w + w * w)) 150 = 2(-3 + 3w + (-1w + w2)) Combine like terms: 3w + -1w = 2w 150 = 2(-3 + 2w + w2) 150 = (-3 * 2 + 2w * 2 + w2 * 2) 150 = (-6 + 4w + 2w2) Solving 150 = -6 + 4w + 2w2 Solving for variable 'w'. Combine like terms: 150 + 6 = 156 156 + -4w + -2w2 = -6 + 4w + 2w2 + 6 + -4w + -2w2 Reorder the terms: 156 + -4w + -2w2 = -6 + 6 + 4w + -4w + 2w2 + -2w2 Combine like terms: -6 + 6 = 0 156 + -4w + -2w2 = 0 + 4w + -4w + 2w2 + -2w2 156 + -4w + -2w2 = 4w + -4w + 2w2 + -2w2 Combine like terms: 4w + -4w = 0 156 + -4w + -2w2 = 0 + 2w2 + -2w2 156 + -4w + -2w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 156 + -4w + -2w2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(78 + -2w + -1w2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(78 + -2w + -1w2)' equal to zero and attempt to solve: Simplifying 78 + -2w + -1w2 = 0 Solving 78 + -2w + -1w2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -78 + 2w + w2 = 0 Move the constant term to the right: Add '78' to each side of the equation. -78 + 2w + 78 + w2 = 0 + 78 Reorder the terms: -78 + 78 + 2w + w2 = 0 + 78 Combine like terms: -78 + 78 = 0 0 + 2w + w2 = 0 + 78 2w + w2 = 0 + 78 Combine like terms: 0 + 78 = 78 2w + w2 = 78 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 = 78 + 1 Reorder the terms: 1 + 2w + w2 = 78 + 1 Combine like terms: 78 + 1 = 79 1 + 2w + w2 = 79 Factor a perfect square on the left side: (w + 1)(w + 1) = 79 Calculate the square root of the right side: 8.888194417 Break this problem into two subproblems by setting (w + 1) equal to 8.888194417 and -8.888194417.Subproblem 1
w + 1 = 8.888194417 Simplifying w + 1 = 8.888194417 Reorder the terms: 1 + w = 8.888194417 Solving 1 + w = 8.888194417 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 = 8.888194417 + -1 Combine like terms: 1 + -1 = 0 0 + w = 8.888194417 + -1 w = 8.888194417 + -1 Combine like terms: 8.888194417 + -1 = 7.888194417 w = 7.888194417 Simplifying w = 7.888194417Subproblem 2
w + 1 = -8.888194417 Simplifying w + 1 = -8.888194417 Reorder the terms: 1 + w = -8.888194417 Solving 1 + w = -8.888194417 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 = -8.888194417 + -1 Combine like terms: 1 + -1 = 0 0 + w = -8.888194417 + -1 w = -8.888194417 + -1 Combine like terms: -8.888194417 + -1 = -9.888194417 w = -9.888194417 Simplifying w = -9.888194417Solution
The solution to the problem is based on the solutions from the subproblems. w = {7.888194417, -9.888194417}Solution
w = {7.888194417, -9.888194417}
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