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Simplifying x4 + -9x2 + -3 = 0 Reorder the terms: -3 + -9x2 + x4 = 0 Solving -3 + -9x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -9x2 + 3 + x4 = 0 + 3 Reorder the terms: -3 + 3 + -9x2 + x4 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -9x2 + x4 = 0 + 3 -9x2 + x4 = 0 + 3 Combine like terms: 0 + 3 = 3 -9x2 + x4 = 3 The x term is -9x2. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x2 + 20.25 + x4 = 3 + 20.25 Reorder the terms: 20.25 + -9x2 + x4 = 3 + 20.25 Combine like terms: 3 + 20.25 = 23.25 20.25 + -9x2 + x4 = 23.25 Factor a perfect square on the left side: (x2 + -4.5)(x2 + -4.5) = 23.25 Calculate the square root of the right side: 4.82182538 Break this problem into two subproblems by setting (x2 + -4.5) equal to 4.82182538 and -4.82182538.Subproblem 1
x2 + -4.5 = 4.82182538 Simplifying x2 + -4.5 = 4.82182538 Reorder the terms: -4.5 + x2 = 4.82182538 Solving -4.5 + x2 = 4.82182538 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x2 = 4.82182538 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x2 = 4.82182538 + 4.5 x2 = 4.82182538 + 4.5 Combine like terms: 4.82182538 + 4.5 = 9.32182538 x2 = 9.32182538 Simplifying x2 = 9.32182538 Take the square root of each side: x = {-3.053166451, 3.053166451}Subproblem 2
x2 + -4.5 = -4.82182538 Simplifying x2 + -4.5 = -4.82182538 Reorder the terms: -4.5 + x2 = -4.82182538 Solving -4.5 + x2 = -4.82182538 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x2 = -4.82182538 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x2 = -4.82182538 + 4.5 x2 = -4.82182538 + 4.5 Combine like terms: -4.82182538 + 4.5 = -0.32182538 x2 = -0.32182538 Simplifying x2 = -0.32182538 Reorder the terms: 0.32182538 + x2 = -0.32182538 + 0.32182538 Combine like terms: -0.32182538 + 0.32182538 = 0.00000000 0.32182538 + x2 = 0.00000000 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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