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Simplifying 0 = 5x4 + 9x2 + 2 Reorder the terms: 0 = 2 + 9x2 + 5x4 Solving 0 = 2 + 9x2 + 5x4 Solving for variable 'x'. Combine like terms: 0 + -2 = -2 -2 + -9x2 + -5x4 = 2 + 9x2 + 5x4 + -2 + -9x2 + -5x4 Reorder the terms: -2 + -9x2 + -5x4 = 2 + -2 + 9x2 + -9x2 + 5x4 + -5x4 Combine like terms: 2 + -2 = 0 -2 + -9x2 + -5x4 = 0 + 9x2 + -9x2 + 5x4 + -5x4 -2 + -9x2 + -5x4 = 9x2 + -9x2 + 5x4 + -5x4 Combine like terms: 9x2 + -9x2 = 0 -2 + -9x2 + -5x4 = 0 + 5x4 + -5x4 -2 + -9x2 + -5x4 = 5x4 + -5x4 Combine like terms: 5x4 + -5x4 = 0 -2 + -9x2 + -5x4 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(2 + 9x2 + 5x4) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(2 + 9x2 + 5x4)' equal to zero and attempt to solve: Simplifying 2 + 9x2 + 5x4 = 0 Solving 2 + 9x2 + 5x4 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.4 + 1.8x2 + x4 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + 1.8x2 + -0.4 + x4 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + 1.8x2 + x4 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + 1.8x2 + x4 = 0 + -0.4 1.8x2 + x4 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 1.8x2 + x4 = -0.4 The x term is 1.8x2. Take half its coefficient (0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. 1.8x2 + 0.81 + x4 = -0.4 + 0.81 Reorder the terms: 0.81 + 1.8x2 + x4 = -0.4 + 0.81 Combine like terms: -0.4 + 0.81 = 0.41 0.81 + 1.8x2 + x4 = 0.41 Factor a perfect square on the left side: (x2 + 0.9)(x2 + 0.9) = 0.41 Calculate the square root of the right side: 0.640312424 Break this problem into two subproblems by setting (x2 + 0.9) equal to 0.640312424 and -0.640312424.Subproblem 1
x2 + 0.9 = 0.640312424 Simplifying x2 + 0.9 = 0.640312424 Reorder the terms: 0.9 + x2 = 0.640312424 Solving 0.9 + x2 = 0.640312424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + x2 = 0.640312424 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x2 = 0.640312424 + -0.9 x2 = 0.640312424 + -0.9 Combine like terms: 0.640312424 + -0.9 = -0.259687576 x2 = -0.259687576 Simplifying x2 = -0.259687576 Reorder the terms: 0.259687576 + x2 = -0.259687576 + 0.259687576 Combine like terms: -0.259687576 + 0.259687576 = 0.000000000 0.259687576 + 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 + 0.9 = -0.640312424 Simplifying x2 + 0.9 = -0.640312424 Reorder the terms: 0.9 + x2 = -0.640312424 Solving 0.9 + x2 = -0.640312424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + x2 = -0.640312424 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x2 = -0.640312424 + -0.9 x2 = -0.640312424 + -0.9 Combine like terms: -0.640312424 + -0.9 = -1.540312424 x2 = -1.540312424 Simplifying x2 = -1.540312424 Reorder the terms: 1.540312424 + x2 = -1.540312424 + 1.540312424 Combine like terms: -1.540312424 + 1.540312424 = 0.000000000 1.540312424 + 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. 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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