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Simplifying (2w + -6.4)(4w + -8.4) = 0 Reorder the terms: (-6.4 + 2w)(4w + -8.4) = 0 Reorder the terms: (-6.4 + 2w)(-8.4 + 4w) = 0 Multiply (-6.4 + 2w) * (-8.4 + 4w) (-6.4(-8.4 + 4w) + 2w * (-8.4 + 4w)) = 0 ((-8.4 * -6.4 + 4w * -6.4) + 2w * (-8.4 + 4w)) = 0 ((53.76 + -25.6w) + 2w * (-8.4 + 4w)) = 0 (53.76 + -25.6w + (-8.4 * 2w + 4w * 2w)) = 0 (53.76 + -25.6w + (-16.8w + 8w2)) = 0 Combine like terms: -25.6w + -16.8w = -42.4w (53.76 + -42.4w + 8w2) = 0 Solving 53.76 + -42.4w + 8w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 6.72 + -5.3w + w2 = 0 Move the constant term to the right: Add '-6.72' to each side of the equation. 6.72 + -5.3w + -6.72 + w2 = 0 + -6.72 Reorder the terms: 6.72 + -6.72 + -5.3w + w2 = 0 + -6.72 Combine like terms: 6.72 + -6.72 = 0.00 0.00 + -5.3w + w2 = 0 + -6.72 -5.3w + w2 = 0 + -6.72 Combine like terms: 0 + -6.72 = -6.72 -5.3w + w2 = -6.72 The w term is -5.3w. Take half its coefficient (-2.65). Square it (7.0225) and add it to both sides. Add '7.0225' to each side of the equation. -5.3w + 7.0225 + w2 = -6.72 + 7.0225 Reorder the terms: 7.0225 + -5.3w + w2 = -6.72 + 7.0225 Combine like terms: -6.72 + 7.0225 = 0.3025 7.0225 + -5.3w + w2 = 0.3025 Factor a perfect square on the left side: (w + -2.65)(w + -2.65) = 0.3025 Calculate the square root of the right side: 0.55 Break this problem into two subproblems by setting (w + -2.65) equal to 0.55 and -0.55.Subproblem 1
w + -2.65 = 0.55 Simplifying w + -2.65 = 0.55 Reorder the terms: -2.65 + w = 0.55 Solving -2.65 + w = 0.55 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2.65' to each side of the equation. -2.65 + 2.65 + w = 0.55 + 2.65 Combine like terms: -2.65 + 2.65 = 0.00 0.00 + w = 0.55 + 2.65 w = 0.55 + 2.65 Combine like terms: 0.55 + 2.65 = 3.2 w = 3.2 Simplifying w = 3.2Subproblem 2
w + -2.65 = -0.55 Simplifying w + -2.65 = -0.55 Reorder the terms: -2.65 + w = -0.55 Solving -2.65 + w = -0.55 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2.65' to each side of the equation. -2.65 + 2.65 + w = -0.55 + 2.65 Combine like terms: -2.65 + 2.65 = 0.00 0.00 + w = -0.55 + 2.65 w = -0.55 + 2.65 Combine like terms: -0.55 + 2.65 = 2.1 w = 2.1 Simplifying w = 2.1Solution
The solution to the problem is based on the solutions from the subproblems. w = {3.2, 2.1}
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