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Simplifying 9n2 + 6n + 10 = 0 Reorder the terms: 10 + 6n + 9n2 = 0 Solving 10 + 6n + 9n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 1.111111111 + 0.6666666667n + n2 = 0 Move the constant term to the right: Add '-1.111111111' to each side of the equation. 1.111111111 + 0.6666666667n + -1.111111111 + n2 = 0 + -1.111111111 Reorder the terms: 1.111111111 + -1.111111111 + 0.6666666667n + n2 = 0 + -1.111111111 Combine like terms: 1.111111111 + -1.111111111 = 0.000000000 0.000000000 + 0.6666666667n + n2 = 0 + -1.111111111 0.6666666667n + n2 = 0 + -1.111111111 Combine like terms: 0 + -1.111111111 = -1.111111111 0.6666666667n + n2 = -1.111111111 The n term is 0.6666666667n. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667n + 0.1111111112 + n2 = -1.111111111 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667n + n2 = -1.111111111 + 0.1111111112 Combine like terms: -1.111111111 + 0.1111111112 = -0.9999999998 0.1111111112 + 0.6666666667n + n2 = -0.9999999998 Factor a perfect square on the left side: (n + 0.3333333334)(n + 0.3333333334) = -0.9999999998 Can't calculate square root of the right side. The solution to this equation could not be determined.
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