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Simplifying 9x4 + -3x2 + -4 = 0 Reorder the terms: -4 + -3x2 + 9x4 = 0 Solving -4 + -3x2 + 9x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.4444444444 + -0.3333333333x2 + x4 = 0 Move the constant term to the right: Add '0.4444444444' to each side of the equation. -0.4444444444 + -0.3333333333x2 + 0.4444444444 + x4 = 0 + 0.4444444444 Reorder the terms: -0.4444444444 + 0.4444444444 + -0.3333333333x2 + x4 = 0 + 0.4444444444 Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000 0.0000000000 + -0.3333333333x2 + x4 = 0 + 0.4444444444 -0.3333333333x2 + x4 = 0 + 0.4444444444 Combine like terms: 0 + 0.4444444444 = 0.4444444444 -0.3333333333x2 + x4 = 0.4444444444 The x term is -0.3333333333x2. Take half its coefficient (-0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. -0.3333333333x2 + 0.02777777779 + x4 = 0.4444444444 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333x2 + x4 = 0.4444444444 + 0.02777777779 Combine like terms: 0.4444444444 + 0.02777777779 = 0.47222222219 0.02777777779 + -0.3333333333x2 + x4 = 0.47222222219 Factor a perfect square on the left side: (x2 + -0.1666666667)(x2 + -0.1666666667) = 0.47222222219 Calculate the square root of the right side: 0.687184271 Break this problem into two subproblems by setting (x2 + -0.1666666667) equal to 0.687184271 and -0.687184271.Subproblem 1
x2 + -0.1666666667 = 0.687184271 Simplifying x2 + -0.1666666667 = 0.687184271 Reorder the terms: -0.1666666667 + x2 = 0.687184271 Solving -0.1666666667 + x2 = 0.687184271 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x2 = 0.687184271 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x2 = 0.687184271 + 0.1666666667 x2 = 0.687184271 + 0.1666666667 Combine like terms: 0.687184271 + 0.1666666667 = 0.8538509377 x2 = 0.8538509377 Simplifying x2 = 0.8538509377 Take the square root of each side: x = {-0.92404055, 0.92404055}Subproblem 2
x2 + -0.1666666667 = -0.687184271 Simplifying x2 + -0.1666666667 = -0.687184271 Reorder the terms: -0.1666666667 + x2 = -0.687184271 Solving -0.1666666667 + x2 = -0.687184271 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x2 = -0.687184271 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x2 = -0.687184271 + 0.1666666667 x2 = -0.687184271 + 0.1666666667 Combine like terms: -0.687184271 + 0.1666666667 = -0.5205176043 x2 = -0.5205176043 Simplifying x2 = -0.5205176043 Reorder the terms: 0.5205176043 + x2 = -0.5205176043 + 0.5205176043 Combine like terms: -0.5205176043 + 0.5205176043 = 0.0000000000 0.5205176043 + x2 = 0.0000000000 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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