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Simplifying 8w2 + -7w + -5 = 0 Reorder the terms: -5 + -7w + 8w2 = 0 Solving -5 + -7w + 8w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.625 + -0.875w + w2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + -0.875w + 0.625 + w2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + -0.875w + w2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + -0.875w + w2 = 0 + 0.625 -0.875w + w2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 -0.875w + w2 = 0.625 The w term is -0.875w. Take half its coefficient (-0.4375). Square it (0.19140625) and add it to both sides. Add '0.19140625' to each side of the equation. -0.875w + 0.19140625 + w2 = 0.625 + 0.19140625 Reorder the terms: 0.19140625 + -0.875w + w2 = 0.625 + 0.19140625 Combine like terms: 0.625 + 0.19140625 = 0.81640625 0.19140625 + -0.875w + w2 = 0.81640625 Factor a perfect square on the left side: (w + -0.4375)(w + -0.4375) = 0.81640625 Calculate the square root of the right side: 0.903552018 Break this problem into two subproblems by setting (w + -0.4375) equal to 0.903552018 and -0.903552018.Subproblem 1
w + -0.4375 = 0.903552018 Simplifying w + -0.4375 = 0.903552018 Reorder the terms: -0.4375 + w = 0.903552018 Solving -0.4375 + w = 0.903552018 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + w = 0.903552018 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + w = 0.903552018 + 0.4375 w = 0.903552018 + 0.4375 Combine like terms: 0.903552018 + 0.4375 = 1.341052018 w = 1.341052018 Simplifying w = 1.341052018Subproblem 2
w + -0.4375 = -0.903552018 Simplifying w + -0.4375 = -0.903552018 Reorder the terms: -0.4375 + w = -0.903552018 Solving -0.4375 + w = -0.903552018 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + w = -0.903552018 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + w = -0.903552018 + 0.4375 w = -0.903552018 + 0.4375 Combine like terms: -0.903552018 + 0.4375 = -0.466052018 w = -0.466052018 Simplifying w = -0.466052018Solution
The solution to the problem is based on the solutions from the subproblems. w = {1.341052018, -0.466052018}
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