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Simplifying 0 = x4 + -18x2 + 20 Reorder the terms: 0 = 20 + -18x2 + x4 Solving 0 = 20 + -18x2 + x4 Solving for variable 'x'. Combine like terms: 0 + -20 = -20 -20 + 18x2 + -1x4 = 20 + -18x2 + x4 + -20 + 18x2 + -1x4 Reorder the terms: -20 + 18x2 + -1x4 = 20 + -20 + -18x2 + 18x2 + x4 + -1x4 Combine like terms: 20 + -20 = 0 -20 + 18x2 + -1x4 = 0 + -18x2 + 18x2 + x4 + -1x4 -20 + 18x2 + -1x4 = -18x2 + 18x2 + x4 + -1x4 Combine like terms: -18x2 + 18x2 = 0 -20 + 18x2 + -1x4 = 0 + x4 + -1x4 -20 + 18x2 + -1x4 = x4 + -1x4 Combine like terms: x4 + -1x4 = 0 -20 + 18x2 + -1x4 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 20 + -18x2 + x4 = 0 Move the constant term to the right: Add '-20' to each side of the equation. 20 + -18x2 + -20 + x4 = 0 + -20 Reorder the terms: 20 + -20 + -18x2 + x4 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -18x2 + x4 = 0 + -20 -18x2 + x4 = 0 + -20 Combine like terms: 0 + -20 = -20 -18x2 + x4 = -20 The x term is -18x2. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18x2 + 81 + x4 = -20 + 81 Reorder the terms: 81 + -18x2 + x4 = -20 + 81 Combine like terms: -20 + 81 = 61 81 + -18x2 + x4 = 61 Factor a perfect square on the left side: (x2 + -9)(x2 + -9) = 61 Calculate the square root of the right side: 7.810249676 Break this problem into two subproblems by setting (x2 + -9) equal to 7.810249676 and -7.810249676.Subproblem 1
x2 + -9 = 7.810249676 Simplifying x2 + -9 = 7.810249676 Reorder the terms: -9 + x2 = 7.810249676 Solving -9 + x2 = 7.810249676 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x2 = 7.810249676 + 9 Combine like terms: -9 + 9 = 0 0 + x2 = 7.810249676 + 9 x2 = 7.810249676 + 9 Combine like terms: 7.810249676 + 9 = 16.810249676 x2 = 16.810249676 Simplifying x2 = 16.810249676 Take the square root of each side: x = {-4.100030448, 4.100030448}Subproblem 2
x2 + -9 = -7.810249676 Simplifying x2 + -9 = -7.810249676 Reorder the terms: -9 + x2 = -7.810249676 Solving -9 + x2 = -7.810249676 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x2 = -7.810249676 + 9 Combine like terms: -9 + 9 = 0 0 + x2 = -7.810249676 + 9 x2 = -7.810249676 + 9 Combine like terms: -7.810249676 + 9 = 1.189750324 x2 = 1.189750324 Simplifying x2 = 1.189750324 Take the square root of each side: x = {-1.090756767, 1.090756767}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.100030448, 4.100030448, -1.090756767, 1.090756767}
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