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Simplifying 5x4 + -24x2 + 27 = 0 Reorder the terms: 27 + -24x2 + 5x4 = 0 Solving 27 + -24x2 + 5x4 = 0 Solving for variable 'x'. Factor a trinomial. (9 + -5x2)(3 + -1x2) = 0Subproblem 1
Set the factor '(9 + -5x2)' equal to zero and attempt to solve: Simplifying 9 + -5x2 = 0 Solving 9 + -5x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -5x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -5x2 = 0 + -9 -5x2 = 0 + -9 Combine like terms: 0 + -9 = -9 -5x2 = -9 Divide each side by '-5'. x2 = 1.8 Simplifying x2 = 1.8 Take the square root of each side: x = {-1.341640787, 1.341640787}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 = {-1.341640787, 1.341640787, -1.732050808, 1.732050808}
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