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Simplifying 2x4 + 9x2 + -20 = 0 Reorder the terms: -20 + 9x2 + 2x4 = 0 Solving -20 + 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'. -10 + 4.5x2 + x4 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + 4.5x2 + 10 + x4 = 0 + 10 Reorder the terms: -10 + 10 + 4.5x2 + x4 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 4.5x2 + x4 = 0 + 10 4.5x2 + x4 = 0 + 10 Combine like terms: 0 + 10 = 10 4.5x2 + x4 = 10 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 = 10 + 5.0625 Reorder the terms: 5.0625 + 4.5x2 + x4 = 10 + 5.0625 Combine like terms: 10 + 5.0625 = 15.0625 5.0625 + 4.5x2 + x4 = 15.0625 Factor a perfect square on the left side: (x2 + 2.25)(x2 + 2.25) = 15.0625 Calculate the square root of the right side: 3.881043674 Break this problem into two subproblems by setting (x2 + 2.25) equal to 3.881043674 and -3.881043674.Subproblem 1
x2 + 2.25 = 3.881043674 Simplifying x2 + 2.25 = 3.881043674 Reorder the terms: 2.25 + x2 = 3.881043674 Solving 2.25 + x2 = 3.881043674 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 = 3.881043674 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x2 = 3.881043674 + -2.25 x2 = 3.881043674 + -2.25 Combine like terms: 3.881043674 + -2.25 = 1.631043674 x2 = 1.631043674 Simplifying x2 = 1.631043674 Take the square root of each side: x = {-1.277123202, 1.277123202}Subproblem 2
x2 + 2.25 = -3.881043674 Simplifying x2 + 2.25 = -3.881043674 Reorder the terms: 2.25 + x2 = -3.881043674 Solving 2.25 + x2 = -3.881043674 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 = -3.881043674 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x2 = -3.881043674 + -2.25 x2 = -3.881043674 + -2.25 Combine like terms: -3.881043674 + -2.25 = -6.131043674 x2 = -6.131043674 Simplifying x2 = -6.131043674 Reorder the terms: 6.131043674 + x2 = -6.131043674 + 6.131043674 Combine like terms: -6.131043674 + 6.131043674 = 0.000000000 6.131043674 + 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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