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Simplifying 14x4 + -23x2 + 8 = 0 Reorder the terms: 8 + -23x2 + 14x4 = 0 Solving 8 + -23x2 + 14x4 = 0 Solving for variable 'x'. Factor a trinomial. (1 + -2x2)(8 + -7x2) = 0Subproblem 1
Set the factor '(1 + -2x2)' equal to zero and attempt to solve: Simplifying 1 + -2x2 = 0 Solving 1 + -2x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x2 = 0 + -1 -2x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -2x2 = -1 Divide each side by '-2'. x2 = 0.5 Simplifying x2 = 0.5 Take the square root of each side: x = {-0.707106781, 0.707106781}Subproblem 2
Set the factor '(8 + -7x2)' equal to zero and attempt to solve: Simplifying 8 + -7x2 = 0 Solving 8 + -7x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -7x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -7x2 = 0 + -8 -7x2 = 0 + -8 Combine like terms: 0 + -8 = -8 -7x2 = -8 Divide each side by '-7'. x2 = 1.142857143 Simplifying x2 = 1.142857143 Take the square root of each side: x = {-1.069044968, 1.069044968}Solution
x = {-0.707106781, 0.707106781, -1.069044968, 1.069044968}
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