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Simplifying (w + 1.2)(w + -7.1) = 0 Reorder the terms: (1.2 + w)(w + -7.1) = 0 Reorder the terms: (1.2 + w)(-7.1 + w) = 0 Multiply (1.2 + w) * (-7.1 + w) (1.2(-7.1 + w) + w(-7.1 + w)) = 0 ((-7.1 * 1.2 + w * 1.2) + w(-7.1 + w)) = 0 ((-8.52 + 1.2w) + w(-7.1 + w)) = 0 (-8.52 + 1.2w + (-7.1 * w + w * w)) = 0 (-8.52 + 1.2w + (-7.1w + w2)) = 0 Combine like terms: 1.2w + -7.1w = -5.9w (-8.52 + -5.9w + w2) = 0 Solving -8.52 + -5.9w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '8.52' to each side of the equation. -8.52 + -5.9w + 8.52 + w2 = 0 + 8.52 Reorder the terms: -8.52 + 8.52 + -5.9w + w2 = 0 + 8.52 Combine like terms: -8.52 + 8.52 = 0.00 0.00 + -5.9w + w2 = 0 + 8.52 -5.9w + w2 = 0 + 8.52 Combine like terms: 0 + 8.52 = 8.52 -5.9w + w2 = 8.52 The w term is -5.9w. Take half its coefficient (-2.95). Square it (8.7025) and add it to both sides. Add '8.7025' to each side of the equation. -5.9w + 8.7025 + w2 = 8.52 + 8.7025 Reorder the terms: 8.7025 + -5.9w + w2 = 8.52 + 8.7025 Combine like terms: 8.52 + 8.7025 = 17.2225 8.7025 + -5.9w + w2 = 17.2225 Factor a perfect square on the left side: (w + -2.95)(w + -2.95) = 17.2225 Calculate the square root of the right side: 4.15 Break this problem into two subproblems by setting (w + -2.95) equal to 4.15 and -4.15.Subproblem 1
w + -2.95 = 4.15 Simplifying w + -2.95 = 4.15 Reorder the terms: -2.95 + w = 4.15 Solving -2.95 + w = 4.15 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2.95' to each side of the equation. -2.95 + 2.95 + w = 4.15 + 2.95 Combine like terms: -2.95 + 2.95 = 0.00 0.00 + w = 4.15 + 2.95 w = 4.15 + 2.95 Combine like terms: 4.15 + 2.95 = 7.1 w = 7.1 Simplifying w = 7.1Subproblem 2
w + -2.95 = -4.15 Simplifying w + -2.95 = -4.15 Reorder the terms: -2.95 + w = -4.15 Solving -2.95 + w = -4.15 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2.95' to each side of the equation. -2.95 + 2.95 + w = -4.15 + 2.95 Combine like terms: -2.95 + 2.95 = 0.00 0.00 + w = -4.15 + 2.95 w = -4.15 + 2.95 Combine like terms: -4.15 + 2.95 = -1.2 w = -1.2 Simplifying w = -1.2Solution
The solution to the problem is based on the solutions from the subproblems. w = {7.1, -1.2}
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