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Simplifying x4 + 20x2 + 63 = 0 Reorder the terms: 63 + 20x2 + x4 = 0 Solving 63 + 20x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-63' to each side of the equation. 63 + 20x2 + -63 + x4 = 0 + -63 Reorder the terms: 63 + -63 + 20x2 + x4 = 0 + -63 Combine like terms: 63 + -63 = 0 0 + 20x2 + x4 = 0 + -63 20x2 + x4 = 0 + -63 Combine like terms: 0 + -63 = -63 20x2 + x4 = -63 The x term is 20x2. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x2 + 100 + x4 = -63 + 100 Reorder the terms: 100 + 20x2 + x4 = -63 + 100 Combine like terms: -63 + 100 = 37 100 + 20x2 + x4 = 37 Factor a perfect square on the left side: (x2 + 10)(x2 + 10) = 37 Calculate the square root of the right side: 6.08276253 Break this problem into two subproblems by setting (x2 + 10) equal to 6.08276253 and -6.08276253.Subproblem 1
x2 + 10 = 6.08276253 Simplifying x2 + 10 = 6.08276253 Reorder the terms: 10 + x2 = 6.08276253 Solving 10 + x2 = 6.08276253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x2 = 6.08276253 + -10 Combine like terms: 10 + -10 = 0 0 + x2 = 6.08276253 + -10 x2 = 6.08276253 + -10 Combine like terms: 6.08276253 + -10 = -3.91723747 x2 = -3.91723747 Simplifying x2 = -3.91723747 Reorder the terms: 3.91723747 + x2 = -3.91723747 + 3.91723747 Combine like terms: -3.91723747 + 3.91723747 = 0.00000000 3.91723747 + x2 = 0.00000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x2 + 10 = -6.08276253 Simplifying x2 + 10 = -6.08276253 Reorder the terms: 10 + x2 = -6.08276253 Solving 10 + x2 = -6.08276253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x2 = -6.08276253 + -10 Combine like terms: 10 + -10 = 0 0 + x2 = -6.08276253 + -10 x2 = -6.08276253 + -10 Combine like terms: -6.08276253 + -10 = -16.08276253 x2 = -16.08276253 Simplifying x2 = -16.08276253 Reorder the terms: 16.08276253 + x2 = -16.08276253 + 16.08276253 Combine like terms: -16.08276253 + 16.08276253 = 0.00000000 16.08276253 + x2 = 0.00000000 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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