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Simplifying 11x4 + 8x2 = 1 Reorder the terms: 8x2 + 11x4 = 1 Solving 8x2 + 11x4 = 1 Solving for variable 'x'. Reorder the terms: -1 + 8x2 + 11x4 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + 8x2 + 11x4 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.09090909091 + 0.7272727273x2 + x4 = 0 Move the constant term to the right: Add '0.09090909091' to each side of the equation. -0.09090909091 + 0.7272727273x2 + 0.09090909091 + x4 = 0 + 0.09090909091 Reorder the terms: -0.09090909091 + 0.09090909091 + 0.7272727273x2 + x4 = 0 + 0.09090909091 Combine like terms: -0.09090909091 + 0.09090909091 = 0.00000000000 0.00000000000 + 0.7272727273x2 + x4 = 0 + 0.09090909091 0.7272727273x2 + x4 = 0 + 0.09090909091 Combine like terms: 0 + 0.09090909091 = 0.09090909091 0.7272727273x2 + x4 = 0.09090909091 The x term is 0.7272727273x2. Take half its coefficient (0.3636363637). Square it (0.1322314050) and add it to both sides. Add '0.1322314050' to each side of the equation. 0.7272727273x2 + 0.1322314050 + x4 = 0.09090909091 + 0.1322314050 Reorder the terms: 0.1322314050 + 0.7272727273x2 + x4 = 0.09090909091 + 0.1322314050 Combine like terms: 0.09090909091 + 0.1322314050 = 0.22314049591 0.1322314050 + 0.7272727273x2 + x4 = 0.22314049591 Factor a perfect square on the left side: (x2 + 0.3636363637)(x2 + 0.3636363637) = 0.22314049591 Calculate the square root of the right side: 0.472377493 Break this problem into two subproblems by setting (x2 + 0.3636363637) equal to 0.472377493 and -0.472377493.Subproblem 1
x2 + 0.3636363637 = 0.472377493 Simplifying x2 + 0.3636363637 = 0.472377493 Reorder the terms: 0.3636363637 + x2 = 0.472377493 Solving 0.3636363637 + x2 = 0.472377493 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3636363637' to each side of the equation. 0.3636363637 + -0.3636363637 + x2 = 0.472377493 + -0.3636363637 Combine like terms: 0.3636363637 + -0.3636363637 = 0.0000000000 0.0000000000 + x2 = 0.472377493 + -0.3636363637 x2 = 0.472377493 + -0.3636363637 Combine like terms: 0.472377493 + -0.3636363637 = 0.1087411293 x2 = 0.1087411293 Simplifying x2 = 0.1087411293 Take the square root of each side: x = {-0.329759199, 0.329759199}Subproblem 2
x2 + 0.3636363637 = -0.472377493 Simplifying x2 + 0.3636363637 = -0.472377493 Reorder the terms: 0.3636363637 + x2 = -0.472377493 Solving 0.3636363637 + x2 = -0.472377493 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3636363637' to each side of the equation. 0.3636363637 + -0.3636363637 + x2 = -0.472377493 + -0.3636363637 Combine like terms: 0.3636363637 + -0.3636363637 = 0.0000000000 0.0000000000 + x2 = -0.472377493 + -0.3636363637 x2 = -0.472377493 + -0.3636363637 Combine like terms: -0.472377493 + -0.3636363637 = -0.8360138567 x2 = -0.8360138567 Simplifying x2 = -0.8360138567 Reorder the terms: 0.8360138567 + x2 = -0.8360138567 + 0.8360138567 Combine like terms: -0.8360138567 + 0.8360138567 = 0.0000000000 0.8360138567 + x2 = 0.0000000000 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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