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Simplifying 7x4 + -33x2 + 36 = 0 Reorder the terms: 36 + -33x2 + 7x4 = 0 Solving 36 + -33x2 + 7x4 = 0 Solving for variable 'x'. Factor a trinomial. (12 + -7x2)(3 + -1x2) = 0Subproblem 1
Set the factor '(12 + -7x2)' equal to zero and attempt to solve: Simplifying 12 + -7x2 = 0 Solving 12 + -7x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -7x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -7x2 = 0 + -12 -7x2 = 0 + -12 Combine like terms: 0 + -12 = -12 -7x2 = -12 Divide each side by '-7'. x2 = 1.714285714 Simplifying x2 = 1.714285714 Take the square root of each side: x = {-1.309307341, 1.309307341}Subproblem 2
Set the factor '(3 + -1x2)' equal to zero and attempt to solve: Simplifying 3 + -1x2 = 0 Solving 3 + -1x2 = 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 + -1x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x2 = 0 + -3 -1x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -1x2 = -3 Divide each side by '-1'. x2 = 3 Simplifying x2 = 3 Take the square root of each side: x = {-1.732050808, 1.732050808}Solution
x = {-1.309307341, 1.309307341, -1.732050808, 1.732050808}
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