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Simplifying 2w2 + -8w + -35 = 0 Reorder the terms: -35 + -8w + 2w2 = 0 Solving -35 + -8w + 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'. -17.5 + -4w + w2 = 0 Move the constant term to the right: Add '17.5' to each side of the equation. -17.5 + -4w + 17.5 + w2 = 0 + 17.5 Reorder the terms: -17.5 + 17.5 + -4w + w2 = 0 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + -4w + w2 = 0 + 17.5 -4w + w2 = 0 + 17.5 Combine like terms: 0 + 17.5 = 17.5 -4w + w2 = 17.5 The w term is -4w. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4w + 4 + w2 = 17.5 + 4 Reorder the terms: 4 + -4w + w2 = 17.5 + 4 Combine like terms: 17.5 + 4 = 21.5 4 + -4w + w2 = 21.5 Factor a perfect square on the left side: (w + -2)(w + -2) = 21.5 Calculate the square root of the right side: 4.636809248 Break this problem into two subproblems by setting (w + -2) equal to 4.636809248 and -4.636809248.Subproblem 1
w + -2 = 4.636809248 Simplifying w + -2 = 4.636809248 Reorder the terms: -2 + w = 4.636809248 Solving -2 + w = 4.636809248 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + w = 4.636809248 + 2 Combine like terms: -2 + 2 = 0 0 + w = 4.636809248 + 2 w = 4.636809248 + 2 Combine like terms: 4.636809248 + 2 = 6.636809248 w = 6.636809248 Simplifying w = 6.636809248Subproblem 2
w + -2 = -4.636809248 Simplifying w + -2 = -4.636809248 Reorder the terms: -2 + w = -4.636809248 Solving -2 + w = -4.636809248 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + w = -4.636809248 + 2 Combine like terms: -2 + 2 = 0 0 + w = -4.636809248 + 2 w = -4.636809248 + 2 Combine like terms: -4.636809248 + 2 = -2.636809248 w = -2.636809248 Simplifying w = -2.636809248Solution
The solution to the problem is based on the solutions from the subproblems. w = {6.636809248, -2.636809248}
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