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Simplifying 4x4 + -65x2 + -16 = 0 Reorder the terms: -16 + -65x2 + 4x4 = 0 Solving -16 + -65x2 + 4x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -4 + -16.25x2 + x4 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -16.25x2 + 4 + x4 = 0 + 4 Reorder the terms: -4 + 4 + -16.25x2 + x4 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -16.25x2 + x4 = 0 + 4 -16.25x2 + x4 = 0 + 4 Combine like terms: 0 + 4 = 4 -16.25x2 + x4 = 4 The x term is -16.25x2. Take half its coefficient (-8.125). Square it (66.015625) and add it to both sides. Add '66.015625' to each side of the equation. -16.25x2 + 66.015625 + x4 = 4 + 66.015625 Reorder the terms: 66.015625 + -16.25x2 + x4 = 4 + 66.015625 Combine like terms: 4 + 66.015625 = 70.015625 66.015625 + -16.25x2 + x4 = 70.015625 Factor a perfect square on the left side: (x2 + -8.125)(x2 + -8.125) = 70.015625 Calculate the square root of the right side: 8.367533986 Break this problem into two subproblems by setting (x2 + -8.125) equal to 8.367533986 and -8.367533986.Subproblem 1
x2 + -8.125 = 8.367533986 Simplifying x2 + -8.125 = 8.367533986 Reorder the terms: -8.125 + x2 = 8.367533986 Solving -8.125 + x2 = 8.367533986 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.125' to each side of the equation. -8.125 + 8.125 + x2 = 8.367533986 + 8.125 Combine like terms: -8.125 + 8.125 = 0.000 0.000 + x2 = 8.367533986 + 8.125 x2 = 8.367533986 + 8.125 Combine like terms: 8.367533986 + 8.125 = 16.492533986 x2 = 16.492533986 Simplifying x2 = 16.492533986 Take the square root of each side: x = {-4.061100096, 4.061100096}Subproblem 2
x2 + -8.125 = -8.367533986 Simplifying x2 + -8.125 = -8.367533986 Reorder the terms: -8.125 + x2 = -8.367533986 Solving -8.125 + x2 = -8.367533986 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.125' to each side of the equation. -8.125 + 8.125 + x2 = -8.367533986 + 8.125 Combine like terms: -8.125 + 8.125 = 0.000 0.000 + x2 = -8.367533986 + 8.125 x2 = -8.367533986 + 8.125 Combine like terms: -8.367533986 + 8.125 = -0.242533986 x2 = -0.242533986 Simplifying x2 = -0.242533986 Reorder the terms: 0.242533986 + x2 = -0.242533986 + 0.242533986 Combine like terms: -0.242533986 + 0.242533986 = 0.000000000 0.242533986 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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