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Simplifying 2x4 + 11x2 + 2 = 0 Reorder the terms: 2 + 11x2 + 2x4 = 0 Solving 2 + 11x2 + 2x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1 + 5.5x2 + x4 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 5.5x2 + -1 + x4 = 0 + -1 Reorder the terms: 1 + -1 + 5.5x2 + x4 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 5.5x2 + x4 = 0 + -1 5.5x2 + x4 = 0 + -1 Combine like terms: 0 + -1 = -1 5.5x2 + x4 = -1 The x term is 5.5x2. Take half its coefficient (2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. 5.5x2 + 7.5625 + x4 = -1 + 7.5625 Reorder the terms: 7.5625 + 5.5x2 + x4 = -1 + 7.5625 Combine like terms: -1 + 7.5625 = 6.5625 7.5625 + 5.5x2 + x4 = 6.5625 Factor a perfect square on the left side: (x2 + 2.75)(x2 + 2.75) = 6.5625 Calculate the square root of the right side: 2.561737691 Break this problem into two subproblems by setting (x2 + 2.75) equal to 2.561737691 and -2.561737691.Subproblem 1
x2 + 2.75 = 2.561737691 Simplifying x2 + 2.75 = 2.561737691 Reorder the terms: 2.75 + x2 = 2.561737691 Solving 2.75 + x2 = 2.561737691 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x2 = 2.561737691 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x2 = 2.561737691 + -2.75 x2 = 2.561737691 + -2.75 Combine like terms: 2.561737691 + -2.75 = -0.188262309 x2 = -0.188262309 Simplifying x2 = -0.188262309 Reorder the terms: 0.188262309 + x2 = -0.188262309 + 0.188262309 Combine like terms: -0.188262309 + 0.188262309 = 0.000000000 0.188262309 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x2 + 2.75 = -2.561737691 Simplifying x2 + 2.75 = -2.561737691 Reorder the terms: 2.75 + x2 = -2.561737691 Solving 2.75 + x2 = -2.561737691 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x2 = -2.561737691 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x2 = -2.561737691 + -2.75 x2 = -2.561737691 + -2.75 Combine like terms: -2.561737691 + -2.75 = -5.311737691 x2 = -5.311737691 Simplifying x2 = -5.311737691 Reorder the terms: 5.311737691 + x2 = -5.311737691 + 5.311737691 Combine like terms: -5.311737691 + 5.311737691 = 0.000000000 5.311737691 + x2 = 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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