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Simplifying 6x2 = x4 + 9 Reorder the terms: 6x2 = 9 + x4 Solving 6x2 = 9 + x4 Solving for variable 'x'. Reorder the terms: -9 + 6x2 + -1x4 = 9 + x4 + -9 + -1x4 Reorder the terms: -9 + 6x2 + -1x4 = 9 + -9 + x4 + -1x4 Combine like terms: 9 + -9 = 0 -9 + 6x2 + -1x4 = 0 + x4 + -1x4 -9 + 6x2 + -1x4 = x4 + -1x4 Combine like terms: x4 + -1x4 = 0 -9 + 6x2 + -1x4 = 0 Factor a trinomial. (-3 + x2)(3 + -1x2) = 0Subproblem 1
Set the factor '(-3 + x2)' equal to zero and attempt to solve: Simplifying -3 + x2 = 0 Solving -3 + x2 = 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 + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x2 = 0 + 3 x2 = 0 + 3 Combine like terms: 0 + 3 = 3 x2 = 3 Simplifying x2 = 3 Take the square root of each side: x = {-1.732050808, 1.732050808}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 = {-1.732050808, 1.732050808, -1.732050808, 1.732050808}
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