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Simplifying 4(625u4 + -100u2 + 4) + 11(25u2 + -2) + -3 = 0 Reorder the terms: 4(4 + -100u2 + 625u4) + 11(25u2 + -2) + -3 = 0 (4 * 4 + -100u2 * 4 + 625u4 * 4) + 11(25u2 + -2) + -3 = 0 (16 + -400u2 + 2500u4) + 11(25u2 + -2) + -3 = 0 Reorder the terms: 16 + -400u2 + 2500u4 + 11(-2 + 25u2) + -3 = 0 16 + -400u2 + 2500u4 + (-2 * 11 + 25u2 * 11) + -3 = 0 16 + -400u2 + 2500u4 + (-22 + 275u2) + -3 = 0 Reorder the terms: 16 + -22 + -3 + -400u2 + 275u2 + 2500u4 = 0 Combine like terms: 16 + -22 = -6 -6 + -3 + -400u2 + 275u2 + 2500u4 = 0 Combine like terms: -6 + -3 = -9 -9 + -400u2 + 275u2 + 2500u4 = 0 Combine like terms: -400u2 + 275u2 = -125u2 -9 + -125u2 + 2500u4 = 0 Solving -9 + -125u2 + 2500u4 = 0 Solving for variable 'u'. Factor a trinomial. (-1 + -25u2)(9 + -100u2) = 0 Factor a difference between two squares. (-1 + -25u2)((3 + 10u)(3 + -10u)) = 0Subproblem 1
Set the factor '(-1 + -25u2)' equal to zero and attempt to solve: Simplifying -1 + -25u2 = 0 Solving -1 + -25u2 = 0 Move all terms containing u to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -25u2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -25u2 = 0 + 1 -25u2 = 0 + 1 Combine like terms: 0 + 1 = 1 -25u2 = 1 Divide each side by '-25'. u2 = -0.04 Simplifying u2 = -0.04 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(3 + 10u)' equal to zero and attempt to solve: Simplifying 3 + 10u = 0 Solving 3 + 10u = 0 Move all terms containing u to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 10u = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 10u = 0 + -3 10u = 0 + -3 Combine like terms: 0 + -3 = -3 10u = -3 Divide each side by '10'. u = -0.3 Simplifying u = -0.3Subproblem 3
Set the factor '(3 + -10u)' equal to zero and attempt to solve: Simplifying 3 + -10u = 0 Solving 3 + -10u = 0 Move all terms containing u to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -10u = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -10u = 0 + -3 -10u = 0 + -3 Combine like terms: 0 + -3 = -3 -10u = -3 Divide each side by '-10'. u = 0.3 Simplifying u = 0.3Solution
u = {-0.3, 0.3}
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