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Simplifying 65 + -255x2 + -4x4 = 0 Solving 65 + -255x2 + -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'. -16.25 + 63.75x2 + x4 = 0 Move the constant term to the right: Add '16.25' to each side of the equation. -16.25 + 63.75x2 + 16.25 + x4 = 0 + 16.25 Reorder the terms: -16.25 + 16.25 + 63.75x2 + x4 = 0 + 16.25 Combine like terms: -16.25 + 16.25 = 0.00 0.00 + 63.75x2 + x4 = 0 + 16.25 63.75x2 + x4 = 0 + 16.25 Combine like terms: 0 + 16.25 = 16.25 63.75x2 + x4 = 16.25 The x term is 63.75x2. Take half its coefficient (31.875). Square it (1016.015625) and add it to both sides. Add '1016.015625' to each side of the equation. 63.75x2 + 1016.015625 + x4 = 16.25 + 1016.015625 Reorder the terms: 1016.015625 + 63.75x2 + x4 = 16.25 + 1016.015625 Combine like terms: 16.25 + 1016.015625 = 1032.265625 1016.015625 + 63.75x2 + x4 = 1032.265625 Factor a perfect square on the left side: (x2 + 31.875)(x2 + 31.875) = 1032.265625 Calculate the square root of the right side: 32.128890815 Break this problem into two subproblems by setting (x2 + 31.875) equal to 32.128890815 and -32.128890815.Subproblem 1
x2 + 31.875 = 32.128890815 Simplifying x2 + 31.875 = 32.128890815 Reorder the terms: 31.875 + x2 = 32.128890815 Solving 31.875 + x2 = 32.128890815 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-31.875' to each side of the equation. 31.875 + -31.875 + x2 = 32.128890815 + -31.875 Combine like terms: 31.875 + -31.875 = 0.000 0.000 + x2 = 32.128890815 + -31.875 x2 = 32.128890815 + -31.875 Combine like terms: 32.128890815 + -31.875 = 0.253890815 x2 = 0.253890815 Simplifying x2 = 0.253890815 Take the square root of each side: x = {-0.503875793, 0.503875793}Subproblem 2
x2 + 31.875 = -32.128890815 Simplifying x2 + 31.875 = -32.128890815 Reorder the terms: 31.875 + x2 = -32.128890815 Solving 31.875 + x2 = -32.128890815 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-31.875' to each side of the equation. 31.875 + -31.875 + x2 = -32.128890815 + -31.875 Combine like terms: 31.875 + -31.875 = 0.000 0.000 + x2 = -32.128890815 + -31.875 x2 = -32.128890815 + -31.875 Combine like terms: -32.128890815 + -31.875 = -64.003890815 x2 = -64.003890815 Simplifying x2 = -64.003890815 Reorder the terms: 64.003890815 + x2 = -64.003890815 + 64.003890815 Combine like terms: -64.003890815 + 64.003890815 = 0.000000000 64.003890815 + 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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