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Simplifying x4 + -48x2 + -27 = 0 Reorder the terms: -27 + -48x2 + x4 = 0 Solving -27 + -48x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + -48x2 + 27 + x4 = 0 + 27 Reorder the terms: -27 + 27 + -48x2 + x4 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -48x2 + x4 = 0 + 27 -48x2 + x4 = 0 + 27 Combine like terms: 0 + 27 = 27 -48x2 + x4 = 27 The x term is -48x2. Take half its coefficient (-24). Square it (576) and add it to both sides. Add '576' to each side of the equation. -48x2 + 576 + x4 = 27 + 576 Reorder the terms: 576 + -48x2 + x4 = 27 + 576 Combine like terms: 27 + 576 = 603 576 + -48x2 + x4 = 603 Factor a perfect square on the left side: (x2 + -24)(x2 + -24) = 603 Calculate the square root of the right side: 24.556058316 Break this problem into two subproblems by setting (x2 + -24) equal to 24.556058316 and -24.556058316.Subproblem 1
x2 + -24 = 24.556058316 Simplifying x2 + -24 = 24.556058316 Reorder the terms: -24 + x2 = 24.556058316 Solving -24 + x2 = 24.556058316 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + x2 = 24.556058316 + 24 Combine like terms: -24 + 24 = 0 0 + x2 = 24.556058316 + 24 x2 = 24.556058316 + 24 Combine like terms: 24.556058316 + 24 = 48.556058316 x2 = 48.556058316 Simplifying x2 = 48.556058316 Take the square root of each side: x = {-6.968217729, 6.968217729}Subproblem 2
x2 + -24 = -24.556058316 Simplifying x2 + -24 = -24.556058316 Reorder the terms: -24 + x2 = -24.556058316 Solving -24 + x2 = -24.556058316 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + x2 = -24.556058316 + 24 Combine like terms: -24 + 24 = 0 0 + x2 = -24.556058316 + 24 x2 = -24.556058316 + 24 Combine like terms: -24.556058316 + 24 = -0.556058316 x2 = -0.556058316 Simplifying x2 = -0.556058316 Reorder the terms: 0.556058316 + x2 = -0.556058316 + 0.556058316 Combine like terms: -0.556058316 + 0.556058316 = 0.000000000 0.556058316 + 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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