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Simplifying 16x8 + -169x4 + 225 = 0 Reorder the terms: 225 + -169x4 + 16x8 = 0 Solving 225 + -169x4 + 16x8 = 0 Solving for variable 'x'. Factor a trinomial. (25 + -16x4)(9 + -1x4) = 0 Factor a difference between two squares. ((5 + 4x2)(5 + -4x2))(9 + -1x4) = 0 Factor a difference between two squares. ((3 + x2)(3 + -1x2))(5 + 4x2)(5 + -4x2) = 0Subproblem 1
Set the factor '(5 + 4x2)' equal to zero and attempt to solve: Simplifying 5 + 4x2 = 0 Solving 5 + 4x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 4x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4x2 = 0 + -5 4x2 = 0 + -5 Combine like terms: 0 + -5 = -5 4x2 = -5 Divide each side by '4'. x2 = -1.25 Simplifying x2 = -1.25 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(5 + -4x2)' equal to zero and attempt to solve: Simplifying 5 + -4x2 = 0 Solving 5 + -4x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -4x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4x2 = 0 + -5 -4x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -4x2 = -5 Divide each side by '-4'. x2 = 1.25 Simplifying x2 = 1.25 Take the square root of each side: x = {-1.118033989, 1.118033989}Subproblem 3
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 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 4
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 = {-1.118033989, 1.118033989, -1.732050808, 1.732050808}
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