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Simplifying 5 + -7w + -2w2 = 0 Solving 5 + -7w + -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'. -2.5 + 3.5w + w2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + 3.5w + 2.5 + w2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + 3.5w + w2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + 3.5w + w2 = 0 + 2.5 3.5w + w2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 3.5w + w2 = 2.5 The w term is 3.5w. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5w + 3.0625 + w2 = 2.5 + 3.0625 Reorder the terms: 3.0625 + 3.5w + w2 = 2.5 + 3.0625 Combine like terms: 2.5 + 3.0625 = 5.5625 3.0625 + 3.5w + w2 = 5.5625 Factor a perfect square on the left side: (w + 1.75)(w + 1.75) = 5.5625 Calculate the square root of the right side: 2.358495283 Break this problem into two subproblems by setting (w + 1.75) equal to 2.358495283 and -2.358495283.Subproblem 1
w + 1.75 = 2.358495283 Simplifying w + 1.75 = 2.358495283 Reorder the terms: 1.75 + w = 2.358495283 Solving 1.75 + w = 2.358495283 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + w = 2.358495283 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + w = 2.358495283 + -1.75 w = 2.358495283 + -1.75 Combine like terms: 2.358495283 + -1.75 = 0.608495283 w = 0.608495283 Simplifying w = 0.608495283Subproblem 2
w + 1.75 = -2.358495283 Simplifying w + 1.75 = -2.358495283 Reorder the terms: 1.75 + w = -2.358495283 Solving 1.75 + w = -2.358495283 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + w = -2.358495283 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + w = -2.358495283 + -1.75 w = -2.358495283 + -1.75 Combine like terms: -2.358495283 + -1.75 = -4.108495283 w = -4.108495283 Simplifying w = -4.108495283Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.608495283, -4.108495283}
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