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Simplifying 3w2 + -6w + 2 + w2 + 5w + -6 = 0 Reorder the terms: 2 + -6 + -6w + 5w + 3w2 + w2 = 0 Combine like terms: 2 + -6 = -4 -4 + -6w + 5w + 3w2 + w2 = 0 Combine like terms: -6w + 5w = -1w -4 + -1w + 3w2 + w2 = 0 Combine like terms: 3w2 + w2 = 4w2 -4 + -1w + 4w2 = 0 Solving -4 + -1w + 4w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1 + -0.25w + w2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.25w + 1 + w2 = 0 + 1 Reorder the terms: -1 + 1 + -0.25w + w2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.25w + w2 = 0 + 1 -0.25w + w2 = 0 + 1 Combine like terms: 0 + 1 = 1 -0.25w + w2 = 1 The w term is -0.25w. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25w + 0.015625 + w2 = 1 + 0.015625 Reorder the terms: 0.015625 + -0.25w + w2 = 1 + 0.015625 Combine like terms: 1 + 0.015625 = 1.015625 0.015625 + -0.25w + w2 = 1.015625 Factor a perfect square on the left side: (w + -0.125)(w + -0.125) = 1.015625 Calculate the square root of the right side: 1.007782219 Break this problem into two subproblems by setting (w + -0.125) equal to 1.007782219 and -1.007782219.Subproblem 1
w + -0.125 = 1.007782219 Simplifying w + -0.125 = 1.007782219 Reorder the terms: -0.125 + w = 1.007782219 Solving -0.125 + w = 1.007782219 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + w = 1.007782219 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + w = 1.007782219 + 0.125 w = 1.007782219 + 0.125 Combine like terms: 1.007782219 + 0.125 = 1.132782219 w = 1.132782219 Simplifying w = 1.132782219Subproblem 2
w + -0.125 = -1.007782219 Simplifying w + -0.125 = -1.007782219 Reorder the terms: -0.125 + w = -1.007782219 Solving -0.125 + w = -1.007782219 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + w = -1.007782219 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + w = -1.007782219 + 0.125 w = -1.007782219 + 0.125 Combine like terms: -1.007782219 + 0.125 = -0.882782219 w = -0.882782219 Simplifying w = -0.882782219Solution
The solution to the problem is based on the solutions from the subproblems. w = {1.132782219, -0.882782219}
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