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Simplifying (4w2 + 0.1)(1w2 + -10) = 9 Reorder the terms: (0.1 + 4w2)(1w2 + -10) = 9 Reorder the terms: (0.1 + 4w2)(-10 + 1w2) = 9 Multiply (0.1 + 4w2) * (-10 + 1w2) (0.1(-10 + 1w2) + 4w2 * (-10 + 1w2)) = 9 ((-10 * 0.1 + 1w2 * 0.1) + 4w2 * (-10 + 1w2)) = 9 ((-1 + 0.1w2) + 4w2 * (-10 + 1w2)) = 9 (-1 + 0.1w2 + (-10 * 4w2 + 1w2 * 4w2)) = 9 (-1 + 0.1w2 + (-40w2 + 4w4)) = 9 Combine like terms: 0.1w2 + -40w2 = -39.9w2 (-1 + -39.9w2 + 4w4) = 9 Solving -1 + -39.9w2 + 4w4 = 9 Solving for variable 'w'. Reorder the terms: -1 + -9 + -39.9w2 + 4w4 = 9 + -9 Combine like terms: -1 + -9 = -10 -10 + -39.9w2 + 4w4 = 9 + -9 Combine like terms: 9 + -9 = 0 -10 + -39.9w2 + 4w4 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.5 + -9.975w2 + w4 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -9.975w2 + 2.5 + w4 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -9.975w2 + w4 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -9.975w2 + w4 = 0 + 2.5 -9.975w2 + w4 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -9.975w2 + w4 = 2.5 The w term is -9.975w2. Take half its coefficient (-4.9875). Square it (24.87515625) and add it to both sides. Add '24.87515625' to each side of the equation. -9.975w2 + 24.87515625 + w4 = 2.5 + 24.87515625 Reorder the terms: 24.87515625 + -9.975w2 + w4 = 2.5 + 24.87515625 Combine like terms: 2.5 + 24.87515625 = 27.37515625 24.87515625 + -9.975w2 + w4 = 27.37515625 Factor a perfect square on the left side: (w2 + -4.9875)(w2 + -4.9875) = 27.37515625 Calculate the square root of the right side: 5.232127316 Break this problem into two subproblems by setting (w2 + -4.9875) equal to 5.232127316 and -5.232127316.Subproblem 1
w2 + -4.9875 = 5.232127316 Simplifying w2 + -4.9875 = 5.232127316 Reorder the terms: -4.9875 + w2 = 5.232127316 Solving -4.9875 + w2 = 5.232127316 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '4.9875' to each side of the equation. -4.9875 + 4.9875 + w2 = 5.232127316 + 4.9875 Combine like terms: -4.9875 + 4.9875 = 0.0000 0.0000 + w2 = 5.232127316 + 4.9875 w2 = 5.232127316 + 4.9875 Combine like terms: 5.232127316 + 4.9875 = 10.219627316 w2 = 10.219627316 Simplifying w2 = 10.219627316 Take the square root of each side: w = {-3.196815183, 3.196815183}Subproblem 2
w2 + -4.9875 = -5.232127316 Simplifying w2 + -4.9875 = -5.232127316 Reorder the terms: -4.9875 + w2 = -5.232127316 Solving -4.9875 + w2 = -5.232127316 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '4.9875' to each side of the equation. -4.9875 + 4.9875 + w2 = -5.232127316 + 4.9875 Combine like terms: -4.9875 + 4.9875 = 0.0000 0.0000 + w2 = -5.232127316 + 4.9875 w2 = -5.232127316 + 4.9875 Combine like terms: -5.232127316 + 4.9875 = -0.244627316 w2 = -0.244627316 Simplifying w2 = -0.244627316 Reorder the terms: 0.244627316 + w2 = -0.244627316 + 0.244627316 Combine like terms: -0.244627316 + 0.244627316 = 0.000000000 0.244627316 + w2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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