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Simplifying 2.5w2 = 6w + -3.6 Reorder the terms: 2.5w2 = -3.6 + 6w Solving 2.5w2 = -3.6 + 6w Solving for variable 'w'. Reorder the terms: 3.6 + -6w + 2.5w2 = -3.6 + 6w + 3.6 + -6w Reorder the terms: 3.6 + -6w + 2.5w2 = -3.6 + 3.6 + 6w + -6w Combine like terms: -3.6 + 3.6 = 0.0 3.6 + -6w + 2.5w2 = 0.0 + 6w + -6w 3.6 + -6w + 2.5w2 = 6w + -6w Combine like terms: 6w + -6w = 0 3.6 + -6w + 2.5w2 = 0 Begin completing the square. Divide all terms by 2.5 the coefficient of the squared term: Divide each side by '2.5'. 1.44 + -2.4w + w2 = 0 Move the constant term to the right: Add '-1.44' to each side of the equation. 1.44 + -2.4w + -1.44 + w2 = 0 + -1.44 Reorder the terms: 1.44 + -1.44 + -2.4w + w2 = 0 + -1.44 Combine like terms: 1.44 + -1.44 = 0.00 0.00 + -2.4w + w2 = 0 + -1.44 -2.4w + w2 = 0 + -1.44 Combine like terms: 0 + -1.44 = -1.44 -2.4w + w2 = -1.44 The w term is -2.4w. Take half its coefficient (-1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. -2.4w + 1.44 + w2 = -1.44 + 1.44 Reorder the terms: 1.44 + -2.4w + w2 = -1.44 + 1.44 Combine like terms: -1.44 + 1.44 = 0.00 1.44 + -2.4w + w2 = 0.00 Factor a perfect square on the left side: (w + -1.2)(w + -1.2) = 0.00 Calculate the square root of the right side: 0.00 Break this problem into two subproblems by setting (w + -1.2) equal to 0.00 and 0.00.Subproblem 1
w + -1.2 = 0.00 Simplifying w + -1.2 = 0.00 Reorder the terms: -1.2 + w = 0.00 Solving -1.2 + w = 0.00 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + w = 0.00 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + w = 0.00 + 1.2 w = 0.00 + 1.2 Combine like terms: 0.00 + 1.2 = 1.2 w = 1.2 Simplifying w = 1.2Subproblem 2
w + -1.2 = 0.00 Simplifying w + -1.2 = 0.00 Reorder the terms: -1.2 + w = 0.00 Solving -1.2 + w = 0.00 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + w = 0.00 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + w = 0.00 + 1.2 w = 0.00 + 1.2 Combine like terms: 0.00 + 1.2 = 1.2 w = 1.2 Simplifying w = 1.2Solution
The solution to the problem is based on the solutions from the subproblems. w = {1.2, 1.2}
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