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Simplifying -4(w + -3)(-8 + 2w) = -7w Reorder the terms: -4(-3 + w)(-8 + 2w) = -7w Multiply (-3 + w) * (-8 + 2w) -4(-3(-8 + 2w) + w(-8 + 2w)) = -7w -4((-8 * -3 + 2w * -3) + w(-8 + 2w)) = -7w -4((24 + -6w) + w(-8 + 2w)) = -7w -4(24 + -6w + (-8 * w + 2w * w)) = -7w -4(24 + -6w + (-8w + 2w2)) = -7w Combine like terms: -6w + -8w = -14w -4(24 + -14w + 2w2) = -7w (24 * -4 + -14w * -4 + 2w2 * -4) = -7w (-96 + 56w + -8w2) = -7w Solving -96 + 56w + -8w2 = -7w Solving for variable 'w'. Reorder the terms: -96 + 56w + 7w + -8w2 = -7w + 7w Combine like terms: 56w + 7w = 63w -96 + 63w + -8w2 = -7w + 7w Combine like terms: -7w + 7w = 0 -96 + 63w + -8w2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. 12 + -7.875w + w2 = 0 Move the constant term to the right: Add '-12' to each side of the equation. 12 + -7.875w + -12 + w2 = 0 + -12 Reorder the terms: 12 + -12 + -7.875w + w2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -7.875w + w2 = 0 + -12 -7.875w + w2 = 0 + -12 Combine like terms: 0 + -12 = -12 -7.875w + w2 = -12 The w term is -7.875w. Take half its coefficient (-3.9375). Square it (15.50390625) and add it to both sides. Add '15.50390625' to each side of the equation. -7.875w + 15.50390625 + w2 = -12 + 15.50390625 Reorder the terms: 15.50390625 + -7.875w + w2 = -12 + 15.50390625 Combine like terms: -12 + 15.50390625 = 3.50390625 15.50390625 + -7.875w + w2 = 3.50390625 Factor a perfect square on the left side: (w + -3.9375)(w + -3.9375) = 3.50390625 Calculate the square root of the right side: 1.871872391 Break this problem into two subproblems by setting (w + -3.9375) equal to 1.871872391 and -1.871872391.Subproblem 1
w + -3.9375 = 1.871872391 Simplifying w + -3.9375 = 1.871872391 Reorder the terms: -3.9375 + w = 1.871872391 Solving -3.9375 + w = 1.871872391 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '3.9375' to each side of the equation. -3.9375 + 3.9375 + w = 1.871872391 + 3.9375 Combine like terms: -3.9375 + 3.9375 = 0.0000 0.0000 + w = 1.871872391 + 3.9375 w = 1.871872391 + 3.9375 Combine like terms: 1.871872391 + 3.9375 = 5.809372391 w = 5.809372391 Simplifying w = 5.809372391Subproblem 2
w + -3.9375 = -1.871872391 Simplifying w + -3.9375 = -1.871872391 Reorder the terms: -3.9375 + w = -1.871872391 Solving -3.9375 + w = -1.871872391 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '3.9375' to each side of the equation. -3.9375 + 3.9375 + w = -1.871872391 + 3.9375 Combine like terms: -3.9375 + 3.9375 = 0.0000 0.0000 + w = -1.871872391 + 3.9375 w = -1.871872391 + 3.9375 Combine like terms: -1.871872391 + 3.9375 = 2.065627609 w = 2.065627609 Simplifying w = 2.065627609Solution
The solution to the problem is based on the solutions from the subproblems. w = {5.809372391, 2.065627609}
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