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Simplifying X4 + -40X2 + -33 = 0 Reorder the terms: -33 + -40X2 + X4 = 0 Solving -33 + -40X2 + X4 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '33' to each side of the equation. -33 + -40X2 + 33 + X4 = 0 + 33 Reorder the terms: -33 + 33 + -40X2 + X4 = 0 + 33 Combine like terms: -33 + 33 = 0 0 + -40X2 + X4 = 0 + 33 -40X2 + X4 = 0 + 33 Combine like terms: 0 + 33 = 33 -40X2 + X4 = 33 The X term is -40X2. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40X2 + 400 + X4 = 33 + 400 Reorder the terms: 400 + -40X2 + X4 = 33 + 400 Combine like terms: 33 + 400 = 433 400 + -40X2 + X4 = 433 Factor a perfect square on the left side: (X2 + -20)(X2 + -20) = 433 Calculate the square root of the right side: 20.808652047 Break this problem into two subproblems by setting (X2 + -20) equal to 20.808652047 and -20.808652047.Subproblem 1
X2 + -20 = 20.808652047 Simplifying X2 + -20 = 20.808652047 Reorder the terms: -20 + X2 = 20.808652047 Solving -20 + X2 = 20.808652047 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + X2 = 20.808652047 + 20 Combine like terms: -20 + 20 = 0 0 + X2 = 20.808652047 + 20 X2 = 20.808652047 + 20 Combine like terms: 20.808652047 + 20 = 40.808652047 X2 = 40.808652047 Simplifying X2 = 40.808652047 Take the square root of each side: X = {-6.388164998, 6.388164998}Subproblem 2
X2 + -20 = -20.808652047 Simplifying X2 + -20 = -20.808652047 Reorder the terms: -20 + X2 = -20.808652047 Solving -20 + X2 = -20.808652047 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + X2 = -20.808652047 + 20 Combine like terms: -20 + 20 = 0 0 + X2 = -20.808652047 + 20 X2 = -20.808652047 + 20 Combine like terms: -20.808652047 + 20 = -0.808652047 X2 = -0.808652047 Simplifying X2 = -0.808652047 Reorder the terms: 0.808652047 + X2 = -0.808652047 + 0.808652047 Combine like terms: -0.808652047 + 0.808652047 = 0.000000000 0.808652047 + 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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