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Simplifying (-2w2 + 4w2 + -4) + (-2w2 + -4w2 + -7) + -1(-6w2 + -5w + 5) = 0 Reorder the terms: (-4 + -2w2 + 4w2) + (-2w2 + -4w2 + -7) + -1(-6w2 + -5w + 5) = 0 Combine like terms: -2w2 + 4w2 = 2w2 (-4 + 2w2) + (-2w2 + -4w2 + -7) + -1(-6w2 + -5w + 5) = 0 Remove parenthesis around (-4 + 2w2) -4 + 2w2 + (-2w2 + -4w2 + -7) + -1(-6w2 + -5w + 5) = 0 Reorder the terms: -4 + 2w2 + (-7 + -2w2 + -4w2) + -1(-6w2 + -5w + 5) = 0 Combine like terms: -2w2 + -4w2 = -6w2 -4 + 2w2 + (-7 + -6w2) + -1(-6w2 + -5w + 5) = 0 Remove parenthesis around (-7 + -6w2) -4 + 2w2 + -7 + -6w2 + -1(-6w2 + -5w + 5) = 0 Reorder the terms: -4 + 2w2 + -7 + -6w2 + -1(5 + -5w + -6w2) = 0 -4 + 2w2 + -7 + -6w2 + (5 * -1 + -5w * -1 + -6w2 * -1) = 0 -4 + 2w2 + -7 + -6w2 + (-5 + 5w + 6w2) = 0 Reorder the terms: -4 + -7 + -5 + 5w + 2w2 + -6w2 + 6w2 = 0 Combine like terms: -4 + -7 = -11 -11 + -5 + 5w + 2w2 + -6w2 + 6w2 = 0 Combine like terms: -11 + -5 = -16 -16 + 5w + 2w2 + -6w2 + 6w2 = 0 Combine like terms: 2w2 + -6w2 = -4w2 -16 + 5w + -4w2 + 6w2 = 0 Combine like terms: -4w2 + 6w2 = 2w2 -16 + 5w + 2w2 = 0 Solving -16 + 5w + 2w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -8 + 2.5w + w2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + 2.5w + 8 + w2 = 0 + 8 Reorder the terms: -8 + 8 + 2.5w + w2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 2.5w + w2 = 0 + 8 2.5w + w2 = 0 + 8 Combine like terms: 0 + 8 = 8 2.5w + w2 = 8 The w term is 2.5w. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5w + 1.5625 + w2 = 8 + 1.5625 Reorder the terms: 1.5625 + 2.5w + w2 = 8 + 1.5625 Combine like terms: 8 + 1.5625 = 9.5625 1.5625 + 2.5w + w2 = 9.5625 Factor a perfect square on the left side: (w + 1.25)(w + 1.25) = 9.5625 Calculate the square root of the right side: 3.092329219 Break this problem into two subproblems by setting (w + 1.25) equal to 3.092329219 and -3.092329219.Subproblem 1
w + 1.25 = 3.092329219 Simplifying w + 1.25 = 3.092329219 Reorder the terms: 1.25 + w = 3.092329219 Solving 1.25 + w = 3.092329219 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + w = 3.092329219 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + w = 3.092329219 + -1.25 w = 3.092329219 + -1.25 Combine like terms: 3.092329219 + -1.25 = 1.842329219 w = 1.842329219 Simplifying w = 1.842329219Subproblem 2
w + 1.25 = -3.092329219 Simplifying w + 1.25 = -3.092329219 Reorder the terms: 1.25 + w = -3.092329219 Solving 1.25 + w = -3.092329219 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + w = -3.092329219 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + w = -3.092329219 + -1.25 w = -3.092329219 + -1.25 Combine like terms: -3.092329219 + -1.25 = -4.342329219 w = -4.342329219 Simplifying w = -4.342329219Solution
The solution to the problem is based on the solutions from the subproblems. w = {1.842329219, -4.342329219}
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