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Simplifying x4 = 10x2 + 2 Reorder the terms: x4 = 2 + 10x2 Solving x4 = 2 + 10x2 Solving for variable 'x'. Reorder the terms: -2 + -10x2 + x4 = 2 + 10x2 + -2 + -10x2 Reorder the terms: -2 + -10x2 + x4 = 2 + -2 + 10x2 + -10x2 Combine like terms: 2 + -2 = 0 -2 + -10x2 + x4 = 0 + 10x2 + -10x2 -2 + -10x2 + x4 = 10x2 + -10x2 Combine like terms: 10x2 + -10x2 = 0 -2 + -10x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + -10x2 + 2 + x4 = 0 + 2 Reorder the terms: -2 + 2 + -10x2 + x4 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -10x2 + x4 = 0 + 2 -10x2 + x4 = 0 + 2 Combine like terms: 0 + 2 = 2 -10x2 + x4 = 2 The x term is -10x2. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x2 + 25 + x4 = 2 + 25 Reorder the terms: 25 + -10x2 + x4 = 2 + 25 Combine like terms: 2 + 25 = 27 25 + -10x2 + x4 = 27 Factor a perfect square on the left side: (x2 + -5)(x2 + -5) = 27 Calculate the square root of the right side: 5.196152423 Break this problem into two subproblems by setting (x2 + -5) equal to 5.196152423 and -5.196152423.Subproblem 1
x2 + -5 = 5.196152423 Simplifying x2 + -5 = 5.196152423 Reorder the terms: -5 + x2 = 5.196152423 Solving -5 + x2 = 5.196152423 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x2 = 5.196152423 + 5 Combine like terms: -5 + 5 = 0 0 + x2 = 5.196152423 + 5 x2 = 5.196152423 + 5 Combine like terms: 5.196152423 + 5 = 10.196152423 x2 = 10.196152423 Simplifying x2 = 10.196152423 Take the square root of each side: x = {-3.193141466, 3.193141466}Subproblem 2
x2 + -5 = -5.196152423 Simplifying x2 + -5 = -5.196152423 Reorder the terms: -5 + x2 = -5.196152423 Solving -5 + x2 = -5.196152423 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x2 = -5.196152423 + 5 Combine like terms: -5 + 5 = 0 0 + x2 = -5.196152423 + 5 x2 = -5.196152423 + 5 Combine like terms: -5.196152423 + 5 = -0.196152423 x2 = -0.196152423 Simplifying x2 = -0.196152423 Reorder the terms: 0.196152423 + x2 = -0.196152423 + 0.196152423 Combine like terms: -0.196152423 + 0.196152423 = 0.000000000 0.196152423 + 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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