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Simplifying x4 + -2020x2 + -64 = 0 Reorder the terms: -64 + -2020x2 + x4 = 0 Solving -64 + -2020x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '64' to each side of the equation. -64 + -2020x2 + 64 + x4 = 0 + 64 Reorder the terms: -64 + 64 + -2020x2 + x4 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + -2020x2 + x4 = 0 + 64 -2020x2 + x4 = 0 + 64 Combine like terms: 0 + 64 = 64 -2020x2 + x4 = 64 The x term is -2020x2. Take half its coefficient (-1010). Square it (1020100) and add it to both sides. Add '1020100' to each side of the equation. -2020x2 + 1020100 + x4 = 64 + 1020100 Reorder the terms: 1020100 + -2020x2 + x4 = 64 + 1020100 Combine like terms: 64 + 1020100 = 1020164 1020100 + -2020x2 + x4 = 1020164 Factor a perfect square on the left side: (x2 + -1010)(x2 + -1010) = 1020164 Calculate the square root of the right side: 1010.031682671 Break this problem into two subproblems by setting (x2 + -1010) equal to 1010.031682671 and -1010.031682671.Subproblem 1
x2 + -1010 = 1010.031682671 Simplifying x2 + -1010 = 1010.031682671 Reorder the terms: -1010 + x2 = 1010.031682671 Solving -1010 + x2 = 1010.031682671 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1010' to each side of the equation. -1010 + 1010 + x2 = 1010.031682671 + 1010 Combine like terms: -1010 + 1010 = 0 0 + x2 = 1010.031682671 + 1010 x2 = 1010.031682671 + 1010 Combine like terms: 1010.031682671 + 1010 = 2020.031682671 x2 = 2020.031682671 Simplifying x2 = 2020.031682671 Take the square root of each side: x = {-44.944762572, 44.944762572}Subproblem 2
x2 + -1010 = -1010.031682671 Simplifying x2 + -1010 = -1010.031682671 Reorder the terms: -1010 + x2 = -1010.031682671 Solving -1010 + x2 = -1010.031682671 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1010' to each side of the equation. -1010 + 1010 + x2 = -1010.031682671 + 1010 Combine like terms: -1010 + 1010 = 0 0 + x2 = -1010.031682671 + 1010 x2 = -1010.031682671 + 1010 Combine like terms: -1010.031682671 + 1010 = -0.031682671 x2 = -0.031682671 Simplifying x2 = -0.031682671 Reorder the terms: 0.031682671 + x2 = -0.031682671 + 0.031682671 Combine like terms: -0.031682671 + 0.031682671 = 0.000000000 0.031682671 + 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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