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Simplifying 0 = 9x4 + -42x2 + -8 Reorder the terms: 0 = -8 + -42x2 + 9x4 Solving 0 = -8 + -42x2 + 9x4 Solving for variable 'x'. Combine like terms: 0 + 8 = 8 8 + 42x2 + -9x4 = -8 + -42x2 + 9x4 + 8 + 42x2 + -9x4 Reorder the terms: 8 + 42x2 + -9x4 = -8 + 8 + -42x2 + 42x2 + 9x4 + -9x4 Combine like terms: -8 + 8 = 0 8 + 42x2 + -9x4 = 0 + -42x2 + 42x2 + 9x4 + -9x4 8 + 42x2 + -9x4 = -42x2 + 42x2 + 9x4 + -9x4 Combine like terms: -42x2 + 42x2 = 0 8 + 42x2 + -9x4 = 0 + 9x4 + -9x4 8 + 42x2 + -9x4 = 9x4 + -9x4 Combine like terms: 9x4 + -9x4 = 0 8 + 42x2 + -9x4 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -0.8888888889 + -4.666666667x2 + x4 = 0 Move the constant term to the right: Add '0.8888888889' to each side of the equation. -0.8888888889 + -4.666666667x2 + 0.8888888889 + x4 = 0 + 0.8888888889 Reorder the terms: -0.8888888889 + 0.8888888889 + -4.666666667x2 + x4 = 0 + 0.8888888889 Combine like terms: -0.8888888889 + 0.8888888889 = 0.0000000000 0.0000000000 + -4.666666667x2 + x4 = 0 + 0.8888888889 -4.666666667x2 + x4 = 0 + 0.8888888889 Combine like terms: 0 + 0.8888888889 = 0.8888888889 -4.666666667x2 + x4 = 0.8888888889 The x term is -4.666666667x2. Take half its coefficient (-2.333333334). Square it (5.444444448) and add it to both sides. Add '5.444444448' to each side of the equation. -4.666666667x2 + 5.444444448 + x4 = 0.8888888889 + 5.444444448 Reorder the terms: 5.444444448 + -4.666666667x2 + x4 = 0.8888888889 + 5.444444448 Combine like terms: 0.8888888889 + 5.444444448 = 6.3333333369 5.444444448 + -4.666666667x2 + x4 = 6.3333333369 Factor a perfect square on the left side: (x2 + -2.333333334)(x2 + -2.333333334) = 6.3333333369 Calculate the square root of the right side: 2.516611479 Break this problem into two subproblems by setting (x2 + -2.333333334) equal to 2.516611479 and -2.516611479.Subproblem 1
x2 + -2.333333334 = 2.516611479 Simplifying x2 + -2.333333334 = 2.516611479 Reorder the terms: -2.333333334 + x2 = 2.516611479 Solving -2.333333334 + x2 = 2.516611479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.333333334' to each side of the equation. -2.333333334 + 2.333333334 + x2 = 2.516611479 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + x2 = 2.516611479 + 2.333333334 x2 = 2.516611479 + 2.333333334 Combine like terms: 2.516611479 + 2.333333334 = 4.849944813 x2 = 4.849944813 Simplifying x2 = 4.849944813 Take the square root of each side: x = {-2.202259025, 2.202259025}Subproblem 2
x2 + -2.333333334 = -2.516611479 Simplifying x2 + -2.333333334 = -2.516611479 Reorder the terms: -2.333333334 + x2 = -2.516611479 Solving -2.333333334 + x2 = -2.516611479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.333333334' to each side of the equation. -2.333333334 + 2.333333334 + x2 = -2.516611479 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + x2 = -2.516611479 + 2.333333334 x2 = -2.516611479 + 2.333333334 Combine like terms: -2.516611479 + 2.333333334 = -0.183278145 x2 = -0.183278145 Simplifying x2 = -0.183278145 Reorder the terms: 0.183278145 + x2 = -0.183278145 + 0.183278145 Combine like terms: -0.183278145 + 0.183278145 = 0.000000000 0.183278145 + 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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