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Simplifying 0 = x4 + -18x2 + 6 Reorder the terms: 0 = 6 + -18x2 + x4 Solving 0 = 6 + -18x2 + x4 Solving for variable 'x'. Combine like terms: 0 + -6 = -6 -6 + 18x2 + -1x4 = 6 + -18x2 + x4 + -6 + 18x2 + -1x4 Reorder the terms: -6 + 18x2 + -1x4 = 6 + -6 + -18x2 + 18x2 + x4 + -1x4 Combine like terms: 6 + -6 = 0 -6 + 18x2 + -1x4 = 0 + -18x2 + 18x2 + x4 + -1x4 -6 + 18x2 + -1x4 = -18x2 + 18x2 + x4 + -1x4 Combine like terms: -18x2 + 18x2 = 0 -6 + 18x2 + -1x4 = 0 + x4 + -1x4 -6 + 18x2 + -1x4 = x4 + -1x4 Combine like terms: x4 + -1x4 = 0 -6 + 18x2 + -1x4 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 6 + -18x2 + x4 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + -18x2 + -6 + x4 = 0 + -6 Reorder the terms: 6 + -6 + -18x2 + x4 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -18x2 + x4 = 0 + -6 -18x2 + x4 = 0 + -6 Combine like terms: 0 + -6 = -6 -18x2 + x4 = -6 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 = -6 + 81 Reorder the terms: 81 + -18x2 + x4 = -6 + 81 Combine like terms: -6 + 81 = 75 81 + -18x2 + x4 = 75 Factor a perfect square on the left side: (x2 + -9)(x2 + -9) = 75 Calculate the square root of the right side: 8.660254038 Break this problem into two subproblems by setting (x2 + -9) equal to 8.660254038 and -8.660254038.Subproblem 1
x2 + -9 = 8.660254038 Simplifying x2 + -9 = 8.660254038 Reorder the terms: -9 + x2 = 8.660254038 Solving -9 + x2 = 8.660254038 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 = 8.660254038 + 9 Combine like terms: -9 + 9 = 0 0 + x2 = 8.660254038 + 9 x2 = 8.660254038 + 9 Combine like terms: 8.660254038 + 9 = 17.660254038 x2 = 17.660254038 Simplifying x2 = 17.660254038 Take the square root of each side: x = {-4.202410503, 4.202410503}Subproblem 2
x2 + -9 = -8.660254038 Simplifying x2 + -9 = -8.660254038 Reorder the terms: -9 + x2 = -8.660254038 Solving -9 + x2 = -8.660254038 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 = -8.660254038 + 9 Combine like terms: -9 + 9 = 0 0 + x2 = -8.660254038 + 9 x2 = -8.660254038 + 9 Combine like terms: -8.660254038 + 9 = 0.339745962 x2 = 0.339745962 Simplifying x2 = 0.339745962 Take the square root of each side: x = {-0.582877313, 0.582877313}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.202410503, 4.202410503, -0.582877313, 0.582877313}
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