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Simplifying 0 = 2w2 + -3w + -10 Reorder the terms: 0 = -10 + -3w + 2w2 Solving 0 = -10 + -3w + 2w2 Solving for variable 'w'. Combine like terms: 0 + 10 = 10 10 + 3w + -2w2 = -10 + -3w + 2w2 + 10 + 3w + -2w2 Reorder the terms: 10 + 3w + -2w2 = -10 + 10 + -3w + 3w + 2w2 + -2w2 Combine like terms: -10 + 10 = 0 10 + 3w + -2w2 = 0 + -3w + 3w + 2w2 + -2w2 10 + 3w + -2w2 = -3w + 3w + 2w2 + -2w2 Combine like terms: -3w + 3w = 0 10 + 3w + -2w2 = 0 + 2w2 + -2w2 10 + 3w + -2w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 10 + 3w + -2w2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -5 + -1.5w + w2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -1.5w + 5 + w2 = 0 + 5 Reorder the terms: -5 + 5 + -1.5w + w2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1.5w + w2 = 0 + 5 -1.5w + w2 = 0 + 5 Combine like terms: 0 + 5 = 5 -1.5w + w2 = 5 The w term is -1.5w. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5w + 0.5625 + w2 = 5 + 0.5625 Reorder the terms: 0.5625 + -1.5w + w2 = 5 + 0.5625 Combine like terms: 5 + 0.5625 = 5.5625 0.5625 + -1.5w + w2 = 5.5625 Factor a perfect square on the left side: (w + -0.75)(w + -0.75) = 5.5625 Calculate the square root of the right side: 2.358495283 Break this problem into two subproblems by setting (w + -0.75) equal to 2.358495283 and -2.358495283.Subproblem 1
w + -0.75 = 2.358495283 Simplifying w + -0.75 = 2.358495283 Reorder the terms: -0.75 + w = 2.358495283 Solving -0.75 + w = 2.358495283 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + w = 2.358495283 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + w = 2.358495283 + 0.75 w = 2.358495283 + 0.75 Combine like terms: 2.358495283 + 0.75 = 3.108495283 w = 3.108495283 Simplifying w = 3.108495283Subproblem 2
w + -0.75 = -2.358495283 Simplifying w + -0.75 = -2.358495283 Reorder the terms: -0.75 + w = -2.358495283 Solving -0.75 + w = -2.358495283 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + w = -2.358495283 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + w = -2.358495283 + 0.75 w = -2.358495283 + 0.75 Combine like terms: -2.358495283 + 0.75 = -1.608495283 w = -1.608495283 Simplifying w = -1.608495283Solution
The solution to the problem is based on the solutions from the subproblems. w = {3.108495283, -1.608495283}
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