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Simplifying 4w2 + -3w + -100 = 0 Reorder the terms: -100 + -3w + 4w2 = 0 Solving -100 + -3w + 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'. -25 + -0.75w + w2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + -0.75w + 25 + w2 = 0 + 25 Reorder the terms: -25 + 25 + -0.75w + w2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -0.75w + w2 = 0 + 25 -0.75w + w2 = 0 + 25 Combine like terms: 0 + 25 = 25 -0.75w + w2 = 25 The w term is -0.75w. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75w + 0.140625 + w2 = 25 + 0.140625 Reorder the terms: 0.140625 + -0.75w + w2 = 25 + 0.140625 Combine like terms: 25 + 0.140625 = 25.140625 0.140625 + -0.75w + w2 = 25.140625 Factor a perfect square on the left side: (w + -0.375)(w + -0.375) = 25.140625 Calculate the square root of the right side: 5.01404278 Break this problem into two subproblems by setting (w + -0.375) equal to 5.01404278 and -5.01404278.Subproblem 1
w + -0.375 = 5.01404278 Simplifying w + -0.375 = 5.01404278 Reorder the terms: -0.375 + w = 5.01404278 Solving -0.375 + w = 5.01404278 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + w = 5.01404278 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + w = 5.01404278 + 0.375 w = 5.01404278 + 0.375 Combine like terms: 5.01404278 + 0.375 = 5.38904278 w = 5.38904278 Simplifying w = 5.38904278Subproblem 2
w + -0.375 = -5.01404278 Simplifying w + -0.375 = -5.01404278 Reorder the terms: -0.375 + w = -5.01404278 Solving -0.375 + w = -5.01404278 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + w = -5.01404278 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + w = -5.01404278 + 0.375 w = -5.01404278 + 0.375 Combine like terms: -5.01404278 + 0.375 = -4.63904278 w = -4.63904278 Simplifying w = -4.63904278Solution
The solution to the problem is based on the solutions from the subproblems. w = {5.38904278, -4.63904278}
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