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Simplifying 2x4 + 9x2 + 3 = 0 Reorder the terms: 3 + 9x2 + 2x4 = 0 Solving 3 + 9x2 + 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 + 4.5x2 + x4 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + 4.5x2 + -1.5 + x4 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + 4.5x2 + x4 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + 4.5x2 + x4 = 0 + -1.5 4.5x2 + x4 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 4.5x2 + x4 = -1.5 The x term is 4.5x2. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5x2 + 5.0625 + x4 = -1.5 + 5.0625 Reorder the terms: 5.0625 + 4.5x2 + x4 = -1.5 + 5.0625 Combine like terms: -1.5 + 5.0625 = 3.5625 5.0625 + 4.5x2 + x4 = 3.5625 Factor a perfect square on the left side: (x2 + 2.25)(x2 + 2.25) = 3.5625 Calculate the square root of the right side: 1.887458609 Break this problem into two subproblems by setting (x2 + 2.25) equal to 1.887458609 and -1.887458609.Subproblem 1
x2 + 2.25 = 1.887458609 Simplifying x2 + 2.25 = 1.887458609 Reorder the terms: 2.25 + x2 = 1.887458609 Solving 2.25 + x2 = 1.887458609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x2 = 1.887458609 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x2 = 1.887458609 + -2.25 x2 = 1.887458609 + -2.25 Combine like terms: 1.887458609 + -2.25 = -0.362541391 x2 = -0.362541391 Simplifying x2 = -0.362541391 Reorder the terms: 0.362541391 + x2 = -0.362541391 + 0.362541391 Combine like terms: -0.362541391 + 0.362541391 = 0.000000000 0.362541391 + 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 + 2.25 = -1.887458609 Simplifying x2 + 2.25 = -1.887458609 Reorder the terms: 2.25 + x2 = -1.887458609 Solving 2.25 + x2 = -1.887458609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x2 = -1.887458609 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x2 = -1.887458609 + -2.25 x2 = -1.887458609 + -2.25 Combine like terms: -1.887458609 + -2.25 = -4.137458609 x2 = -4.137458609 Simplifying x2 = -4.137458609 Reorder the terms: 4.137458609 + x2 = -4.137458609 + 4.137458609 Combine like terms: -4.137458609 + 4.137458609 = 0.000000000 4.137458609 + 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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