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Simplifying 4x6 + -33x4 + -9x2 = 0 Reorder the terms: -9x2 + -33x4 + 4x6 = 0 Solving -9x2 + -33x4 + 4x6 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(-9 + -33x2 + 4x4) = 0Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(-9 + -33x2 + 4x4)' equal to zero and attempt to solve: Simplifying -9 + -33x2 + 4x4 = 0 Solving -9 + -33x2 + 4x4 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.25 + -8.25x2 + x4 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + -8.25x2 + 2.25 + x4 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + -8.25x2 + x4 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + -8.25x2 + x4 = 0 + 2.25 -8.25x2 + x4 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 -8.25x2 + x4 = 2.25 The x term is -8.25x2. Take half its coefficient (-4.125). Square it (17.015625) and add it to both sides. Add '17.015625' to each side of the equation. -8.25x2 + 17.015625 + x4 = 2.25 + 17.015625 Reorder the terms: 17.015625 + -8.25x2 + x4 = 2.25 + 17.015625 Combine like terms: 2.25 + 17.015625 = 19.265625 17.015625 + -8.25x2 + x4 = 19.265625 Factor a perfect square on the left side: (x2 + -4.125)(x2 + -4.125) = 19.265625 Calculate the square root of the right side: 4.389262467 Break this problem into two subproblems by setting (x2 + -4.125) equal to 4.389262467 and -4.389262467.Subproblem 1
x2 + -4.125 = 4.389262467 Simplifying x2 + -4.125 = 4.389262467 Reorder the terms: -4.125 + x2 = 4.389262467 Solving -4.125 + x2 = 4.389262467 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.125' to each side of the equation. -4.125 + 4.125 + x2 = 4.389262467 + 4.125 Combine like terms: -4.125 + 4.125 = 0.000 0.000 + x2 = 4.389262467 + 4.125 x2 = 4.389262467 + 4.125 Combine like terms: 4.389262467 + 4.125 = 8.514262467 x2 = 8.514262467 Simplifying x2 = 8.514262467 Take the square root of each side: x = {-2.917920915, 2.917920915}Subproblem 2
x2 + -4.125 = -4.389262467 Simplifying x2 + -4.125 = -4.389262467 Reorder the terms: -4.125 + x2 = -4.389262467 Solving -4.125 + x2 = -4.389262467 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.125' to each side of the equation. -4.125 + 4.125 + x2 = -4.389262467 + 4.125 Combine like terms: -4.125 + 4.125 = 0.000 0.000 + x2 = -4.389262467 + 4.125 x2 = -4.389262467 + 4.125 Combine like terms: -4.389262467 + 4.125 = -0.264262467 x2 = -0.264262467 Simplifying x2 = -0.264262467 Reorder the terms: 0.264262467 + x2 = -0.264262467 + 0.264262467 Combine like terms: -0.264262467 + 0.264262467 = 0.000000000 0.264262467 + 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.Solution
x = {0}
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