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Simplifying 6n2 + n + 15 + 3n2 + 12n + 5 = 0 Reorder the terms: 15 + 5 + n + 12n + 6n2 + 3n2 = 0 Combine like terms: 15 + 5 = 20 20 + n + 12n + 6n2 + 3n2 = 0 Combine like terms: n + 12n = 13n 20 + 13n + 6n2 + 3n2 = 0 Combine like terms: 6n2 + 3n2 = 9n2 20 + 13n + 9n2 = 0 Solving 20 + 13n + 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'. 2.222222222 + 1.444444444n + n2 = 0 Move the constant term to the right: Add '-2.222222222' to each side of the equation. 2.222222222 + 1.444444444n + -2.222222222 + n2 = 0 + -2.222222222 Reorder the terms: 2.222222222 + -2.222222222 + 1.444444444n + n2 = 0 + -2.222222222 Combine like terms: 2.222222222 + -2.222222222 = 0.000000000 0.000000000 + 1.444444444n + n2 = 0 + -2.222222222 1.444444444n + n2 = 0 + -2.222222222 Combine like terms: 0 + -2.222222222 = -2.222222222 1.444444444n + n2 = -2.222222222 The n term is 1.444444444n. Take half its coefficient (0.722222222). Square it (0.5216049380) and add it to both sides. Add '0.5216049380' to each side of the equation. 1.444444444n + 0.5216049380 + n2 = -2.222222222 + 0.5216049380 Reorder the terms: 0.5216049380 + 1.444444444n + n2 = -2.222222222 + 0.5216049380 Combine like terms: -2.222222222 + 0.5216049380 = -1.700617284 0.5216049380 + 1.444444444n + n2 = -1.700617284 Factor a perfect square on the left side: (n + 0.722222222)(n + 0.722222222) = -1.700617284 Can't calculate square root of the right side. The solution to this equation could not be determined.
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