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Simplifying 0 = x4 + -7x2 + 12 Reorder the terms: 0 = 12 + -7x2 + x4 Solving 0 = 12 + -7x2 + x4 Solving for variable 'x'. Combine like terms: 0 + -12 = -12 -12 + 7x2 + -1x4 = 12 + -7x2 + x4 + -12 + 7x2 + -1x4 Reorder the terms: -12 + 7x2 + -1x4 = 12 + -12 + -7x2 + 7x2 + x4 + -1x4 Combine like terms: 12 + -12 = 0 -12 + 7x2 + -1x4 = 0 + -7x2 + 7x2 + x4 + -1x4 -12 + 7x2 + -1x4 = -7x2 + 7x2 + x4 + -1x4 Combine like terms: -7x2 + 7x2 = 0 -12 + 7x2 + -1x4 = 0 + x4 + -1x4 -12 + 7x2 + -1x4 = x4 + -1x4 Combine like terms: x4 + -1x4 = 0 -12 + 7x2 + -1x4 = 0 Factor a trinomial. (-4 + x2)(3 + -1x2) = 0 Factor a difference between two squares. ((2 + x)(-2 + x))(3 + -1x2) = 0Subproblem 1
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}Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Subproblem 3
Set the factor '(-2 + x)' equal to zero and attempt to solve: Simplifying -2 + x = 0 Solving -2 + x = 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 + x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0 + 2 x = 0 + 2 Combine like terms: 0 + 2 = 2 x = 2 Simplifying x = 2Solution
x = {-1.732050808, 1.732050808, -2, 2}
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