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Simplifying 12x4 + 15x2 = 18 Reorder the terms: 15x2 + 12x4 = 18 Solving 15x2 + 12x4 = 18 Solving for variable 'x'. Reorder the terms: -18 + 15x2 + 12x4 = 18 + -18 Combine like terms: 18 + -18 = 0 -18 + 15x2 + 12x4 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-6 + 5x2 + 4x4) = 0 Factor a trinomial. 3((-2 + -1x2)(3 + -4x2)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-2 + -1x2)' equal to zero and attempt to solve: Simplifying -2 + -1x2 = 0 Solving -2 + -1x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x2 = 0 + 2 -1x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -1x2 = 2 Divide each side by '-1'. x2 = -2 Simplifying x2 = -2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(3 + -4x2)' equal to zero and attempt to solve: Simplifying 3 + -4x2 = 0 Solving 3 + -4x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -4x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4x2 = 0 + -3 -4x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -4x2 = -3 Divide each side by '-4'. x2 = 0.75 Simplifying x2 = 0.75 Take the square root of each side: x = {-0.866025404, 0.866025404}Solution
x = {-0.866025404, 0.866025404}
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