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Simplifying -18x4 + -16x2 + 54 = 0 Reorder the terms: 54 + -16x2 + -18x4 = 0 Solving 54 + -16x2 + -18x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(27 + -8x2 + -9x4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(27 + -8x2 + -9x4)' equal to zero and attempt to solve: Simplifying 27 + -8x2 + -9x4 = 0 Solving 27 + -8x2 + -9x4 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -3 + 0.8888888889x2 + x4 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 0.8888888889x2 + 3 + x4 = 0 + 3 Reorder the terms: -3 + 3 + 0.8888888889x2 + x4 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 0.8888888889x2 + x4 = 0 + 3 0.8888888889x2 + x4 = 0 + 3 Combine like terms: 0 + 3 = 3 0.8888888889x2 + x4 = 3 The x term is 0.8888888889x2. Take half its coefficient (0.4444444445). Square it (0.1975308642) and add it to both sides. Add '0.1975308642' to each side of the equation. 0.8888888889x2 + 0.1975308642 + x4 = 3 + 0.1975308642 Reorder the terms: 0.1975308642 + 0.8888888889x2 + x4 = 3 + 0.1975308642 Combine like terms: 3 + 0.1975308642 = 3.1975308642 0.1975308642 + 0.8888888889x2 + x4 = 3.1975308642 Factor a perfect square on the left side: (x2 + 0.4444444445)(x2 + 0.4444444445) = 3.1975308642 Calculate the square root of the right side: 1.788164104 Break this problem into two subproblems by setting (x2 + 0.4444444445) equal to 1.788164104 and -1.788164104.Subproblem 1
x2 + 0.4444444445 = 1.788164104 Simplifying x2 + 0.4444444445 = 1.788164104 Reorder the terms: 0.4444444445 + x2 = 1.788164104 Solving 0.4444444445 + x2 = 1.788164104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4444444445' to each side of the equation. 0.4444444445 + -0.4444444445 + x2 = 1.788164104 + -0.4444444445 Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000 0.0000000000 + x2 = 1.788164104 + -0.4444444445 x2 = 1.788164104 + -0.4444444445 Combine like terms: 1.788164104 + -0.4444444445 = 1.3437196595 x2 = 1.3437196595 Simplifying x2 = 1.3437196595 Take the square root of each side: x = {-1.159189225, 1.159189225}Subproblem 2
x2 + 0.4444444445 = -1.788164104 Simplifying x2 + 0.4444444445 = -1.788164104 Reorder the terms: 0.4444444445 + x2 = -1.788164104 Solving 0.4444444445 + x2 = -1.788164104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4444444445' to each side of the equation. 0.4444444445 + -0.4444444445 + x2 = -1.788164104 + -0.4444444445 Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000 0.0000000000 + x2 = -1.788164104 + -0.4444444445 x2 = -1.788164104 + -0.4444444445 Combine like terms: -1.788164104 + -0.4444444445 = -2.2326085485 x2 = -2.2326085485 Simplifying x2 = -2.2326085485 Reorder the terms: 2.2326085485 + x2 = -2.2326085485 + 2.2326085485 Combine like terms: -2.2326085485 + 2.2326085485 = 0.0000000000 2.2326085485 + 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. 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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