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Simplifying 1 + 9x2 + x4 = 0 Solving 1 + 9x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + 9x2 + -1 + x4 = 0 + -1 Reorder the terms: 1 + -1 + 9x2 + x4 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 9x2 + x4 = 0 + -1 9x2 + x4 = 0 + -1 Combine like terms: 0 + -1 = -1 9x2 + x4 = -1 The x term is 9x2. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x2 + 20.25 + x4 = -1 + 20.25 Reorder the terms: 20.25 + 9x2 + x4 = -1 + 20.25 Combine like terms: -1 + 20.25 = 19.25 20.25 + 9x2 + x4 = 19.25 Factor a perfect square on the left side: (x2 + 4.5)(x2 + 4.5) = 19.25 Calculate the square root of the right side: 4.387482194 Break this problem into two subproblems by setting (x2 + 4.5) equal to 4.387482194 and -4.387482194.Subproblem 1
x2 + 4.5 = 4.387482194 Simplifying x2 + 4.5 = 4.387482194 Reorder the terms: 4.5 + x2 = 4.387482194 Solving 4.5 + x2 = 4.387482194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x2 = 4.387482194 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x2 = 4.387482194 + -4.5 x2 = 4.387482194 + -4.5 Combine like terms: 4.387482194 + -4.5 = -0.112517806 x2 = -0.112517806 Simplifying x2 = -0.112517806 Reorder the terms: 0.112517806 + x2 = -0.112517806 + 0.112517806 Combine like terms: -0.112517806 + 0.112517806 = 0.000000000 0.112517806 + 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 + 4.5 = -4.387482194 Simplifying x2 + 4.5 = -4.387482194 Reorder the terms: 4.5 + x2 = -4.387482194 Solving 4.5 + x2 = -4.387482194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x2 = -4.387482194 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x2 = -4.387482194 + -4.5 x2 = -4.387482194 + -4.5 Combine like terms: -4.387482194 + -4.5 = -8.887482194 x2 = -8.887482194 Simplifying x2 = -8.887482194 Reorder the terms: 8.887482194 + x2 = -8.887482194 + 8.887482194 Combine like terms: -8.887482194 + 8.887482194 = 0.000000000 8.887482194 + 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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