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Simplifying 9x4 + 9x2 + 1 = 0 Reorder the terms: 1 + 9x2 + 9x4 = 0 Solving 1 + 9x2 + 9x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.1111111111 + x2 + x4 = 0 Move the constant term to the right: Add '-0.1111111111' to each side of the equation. 0.1111111111 + x2 + -0.1111111111 + x4 = 0 + -0.1111111111 Reorder the terms: 0.1111111111 + -0.1111111111 + x2 + x4 = 0 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + x2 + x4 = 0 + -0.1111111111 x2 + x4 = 0 + -0.1111111111 Combine like terms: 0 + -0.1111111111 = -0.1111111111 x2 + x4 = -0.1111111111 The x term is x2. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x4 = -0.1111111111 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x4 = -0.1111111111 + 0.25 Combine like terms: -0.1111111111 + 0.25 = 0.1388888889 1.25 + x4 = 0.1388888889 Factor a perfect square on the left side: (x2 + 0.5)(x2 + 0.5) = 0.1388888889 Calculate the square root of the right side: 0.372677996 Break this problem into two subproblems by setting (x2 + 0.5) equal to 0.372677996 and -0.372677996.Subproblem 1
x2 + 0.5 = 0.372677996 Simplifying x2 + 0.5 = 0.372677996 Reorder the terms: 0.5 + x2 = 0.372677996 Solving 0.5 + x2 = 0.372677996 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x2 = 0.372677996 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = 0.372677996 + -0.5 x2 = 0.372677996 + -0.5 Combine like terms: 0.372677996 + -0.5 = -0.127322004 x2 = -0.127322004 Simplifying x2 = -0.127322004 Reorder the terms: 0.127322004 + x2 = -0.127322004 + 0.127322004 Combine like terms: -0.127322004 + 0.127322004 = 0.000000000 0.127322004 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x2 + 0.5 = -0.372677996 Simplifying x2 + 0.5 = -0.372677996 Reorder the terms: 0.5 + x2 = -0.372677996 Solving 0.5 + x2 = -0.372677996 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x2 = -0.372677996 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = -0.372677996 + -0.5 x2 = -0.372677996 + -0.5 Combine like terms: -0.372677996 + -0.5 = -0.872677996 x2 = -0.872677996 Simplifying x2 = -0.872677996 Reorder the terms: 0.872677996 + x2 = -0.872677996 + 0.872677996 Combine like terms: -0.872677996 + 0.872677996 = 0.000000000 0.872677996 + 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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