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Simplifying 0 = x4 + -18x2 + -4 Reorder the terms: 0 = -4 + -18x2 + x4 Solving 0 = -4 + -18x2 + x4 Solving for variable 'x'. Combine like terms: 0 + 4 = 4 4 + 18x2 + -1x4 = -4 + -18x2 + x4 + 4 + 18x2 + -1x4 Reorder the terms: 4 + 18x2 + -1x4 = -4 + 4 + -18x2 + 18x2 + x4 + -1x4 Combine like terms: -4 + 4 = 0 4 + 18x2 + -1x4 = 0 + -18x2 + 18x2 + x4 + -1x4 4 + 18x2 + -1x4 = -18x2 + 18x2 + x4 + -1x4 Combine like terms: -18x2 + 18x2 = 0 4 + 18x2 + -1x4 = 0 + x4 + -1x4 4 + 18x2 + -1x4 = x4 + -1x4 Combine like terms: x4 + -1x4 = 0 4 + 18x2 + -1x4 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -4 + -18x2 + x4 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -18x2 + 4 + x4 = 0 + 4 Reorder the terms: -4 + 4 + -18x2 + x4 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -18x2 + x4 = 0 + 4 -18x2 + x4 = 0 + 4 Combine like terms: 0 + 4 = 4 -18x2 + x4 = 4 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 = 4 + 81 Reorder the terms: 81 + -18x2 + x4 = 4 + 81 Combine like terms: 4 + 81 = 85 81 + -18x2 + x4 = 85 Factor a perfect square on the left side: (x2 + -9)(x2 + -9) = 85 Calculate the square root of the right side: 9.219544457 Break this problem into two subproblems by setting (x2 + -9) equal to 9.219544457 and -9.219544457.Subproblem 1
x2 + -9 = 9.219544457 Simplifying x2 + -9 = 9.219544457 Reorder the terms: -9 + x2 = 9.219544457 Solving -9 + x2 = 9.219544457 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 = 9.219544457 + 9 Combine like terms: -9 + 9 = 0 0 + x2 = 9.219544457 + 9 x2 = 9.219544457 + 9 Combine like terms: 9.219544457 + 9 = 18.219544457 x2 = 18.219544457 Simplifying x2 = 18.219544457 Take the square root of each side: x = {-4.268435833, 4.268435833}Subproblem 2
x2 + -9 = -9.219544457 Simplifying x2 + -9 = -9.219544457 Reorder the terms: -9 + x2 = -9.219544457 Solving -9 + x2 = -9.219544457 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 = -9.219544457 + 9 Combine like terms: -9 + 9 = 0 0 + x2 = -9.219544457 + 9 x2 = -9.219544457 + 9 Combine like terms: -9.219544457 + 9 = -0.219544457 x2 = -0.219544457 Simplifying x2 = -0.219544457 Reorder the terms: 0.219544457 + x2 = -0.219544457 + 0.219544457 Combine like terms: -0.219544457 + 0.219544457 = 0.000000000 0.219544457 + 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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