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Simplifying 4w4 + -100w2 + 25 = 0 Reorder the terms: 25 + -100w2 + 4w4 = 0 Solving 25 + -100w2 + 4w4 = 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'. 6.25 + -25w2 + w4 = 0 Move the constant term to the right: Add '-6.25' to each side of the equation. 6.25 + -25w2 + -6.25 + w4 = 0 + -6.25 Reorder the terms: 6.25 + -6.25 + -25w2 + w4 = 0 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + -25w2 + w4 = 0 + -6.25 -25w2 + w4 = 0 + -6.25 Combine like terms: 0 + -6.25 = -6.25 -25w2 + w4 = -6.25 The w term is -25w2. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25w2 + 156.25 + w4 = -6.25 + 156.25 Reorder the terms: 156.25 + -25w2 + w4 = -6.25 + 156.25 Combine like terms: -6.25 + 156.25 = 150 156.25 + -25w2 + w4 = 150 Factor a perfect square on the left side: (w2 + -12.5)(w2 + -12.5) = 150 Calculate the square root of the right side: 12.247448714 Break this problem into two subproblems by setting (w2 + -12.5) equal to 12.247448714 and -12.247448714.Subproblem 1
w2 + -12.5 = 12.247448714 Simplifying w2 + -12.5 = 12.247448714 Reorder the terms: -12.5 + w2 = 12.247448714 Solving -12.5 + w2 = 12.247448714 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + w2 = 12.247448714 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + w2 = 12.247448714 + 12.5 w2 = 12.247448714 + 12.5 Combine like terms: 12.247448714 + 12.5 = 24.747448714 w2 = 24.747448714 Simplifying w2 = 24.747448714 Take the square root of each side: w = {-4.974680765, 4.974680765}Subproblem 2
w2 + -12.5 = -12.247448714 Simplifying w2 + -12.5 = -12.247448714 Reorder the terms: -12.5 + w2 = -12.247448714 Solving -12.5 + w2 = -12.247448714 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + w2 = -12.247448714 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + w2 = -12.247448714 + 12.5 w2 = -12.247448714 + 12.5 Combine like terms: -12.247448714 + 12.5 = 0.252551286 w2 = 0.252551286 Simplifying w2 = 0.252551286 Take the square root of each side: w = {-0.50254481, 0.50254481}Solution
The solution to the problem is based on the solutions from the subproblems. w = {-4.974680765, 4.974680765, -0.50254481, 0.50254481}
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