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Simplifying 8n2 + 3n + 10 + 3n2 + -6n + -7 = 0 Reorder the terms: 10 + -7 + 3n + -6n + 8n2 + 3n2 = 0 Combine like terms: 10 + -7 = 3 3 + 3n + -6n + 8n2 + 3n2 = 0 Combine like terms: 3n + -6n = -3n 3 + -3n + 8n2 + 3n2 = 0 Combine like terms: 8n2 + 3n2 = 11n2 3 + -3n + 11n2 = 0 Solving 3 + -3n + 11n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. 0.2727272727 + -0.2727272727n + n2 = 0 Move the constant term to the right: Add '-0.2727272727' to each side of the equation. 0.2727272727 + -0.2727272727n + -0.2727272727 + n2 = 0 + -0.2727272727 Reorder the terms: 0.2727272727 + -0.2727272727 + -0.2727272727n + n2 = 0 + -0.2727272727 Combine like terms: 0.2727272727 + -0.2727272727 = 0.0000000000 0.0000000000 + -0.2727272727n + n2 = 0 + -0.2727272727 -0.2727272727n + n2 = 0 + -0.2727272727 Combine like terms: 0 + -0.2727272727 = -0.2727272727 -0.2727272727n + n2 = -0.2727272727 The n term is -0.2727272727n. Take half its coefficient (-0.1363636364). Square it (0.01859504133) and add it to both sides. Add '0.01859504133' to each side of the equation. -0.2727272727n + 0.01859504133 + n2 = -0.2727272727 + 0.01859504133 Reorder the terms: 0.01859504133 + -0.2727272727n + n2 = -0.2727272727 + 0.01859504133 Combine like terms: -0.2727272727 + 0.01859504133 = -0.25413223137 0.01859504133 + -0.2727272727n + n2 = -0.25413223137 Factor a perfect square on the left side: (n + -0.1363636364)(n + -0.1363636364) = -0.25413223137 Can't calculate square root of the right side. The solution to this equation could not be determined.
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