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Simplifying 81x2 + 18x + 9 = 0 Reorder the terms: 9 + 18x + 81x2 = 0 Solving 9 + 18x + 81x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '9'. 9(1 + 2x + 9x2) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(1 + 2x + 9x2)' equal to zero and attempt to solve: Simplifying 1 + 2x + 9x2 = 0 Solving 1 + 2x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.1111111111 + 0.2222222222x + x2 = 0 Move the constant term to the right: Add '-0.1111111111' to each side of the equation. 0.1111111111 + 0.2222222222x + -0.1111111111 + x2 = 0 + -0.1111111111 Reorder the terms: 0.1111111111 + -0.1111111111 + 0.2222222222x + x2 = 0 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + 0.2222222222x + x2 = 0 + -0.1111111111 0.2222222222x + x2 = 0 + -0.1111111111 Combine like terms: 0 + -0.1111111111 = -0.1111111111 0.2222222222x + x2 = -0.1111111111 The x term is 0.2222222222x. Take half its coefficient (0.1111111111). Square it (0.01234567901) and add it to both sides. Add '0.01234567901' to each side of the equation. 0.2222222222x + 0.01234567901 + x2 = -0.1111111111 + 0.01234567901 Reorder the terms: 0.01234567901 + 0.2222222222x + x2 = -0.1111111111 + 0.01234567901 Combine like terms: -0.1111111111 + 0.01234567901 = -0.09876543209 0.01234567901 + 0.2222222222x + x2 = -0.09876543209 Factor a perfect square on the left side: (x + 0.1111111111)(x + 0.1111111111) = -0.09876543209 Can't calculate square root of the right side. 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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