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Simplifying (4n2 + 5) + -1(-2n2 + 2n + -4) = 0 Reorder the terms: (5 + 4n2) + -1(-2n2 + 2n + -4) = 0 Remove parenthesis around (5 + 4n2) 5 + 4n2 + -1(-2n2 + 2n + -4) = 0 Reorder the terms: 5 + 4n2 + -1(-4 + 2n + -2n2) = 0 5 + 4n2 + (-4 * -1 + 2n * -1 + -2n2 * -1) = 0 5 + 4n2 + (4 + -2n + 2n2) = 0 Reorder the terms: 5 + 4 + -2n + 4n2 + 2n2 = 0 Combine like terms: 5 + 4 = 9 9 + -2n + 4n2 + 2n2 = 0 Combine like terms: 4n2 + 2n2 = 6n2 9 + -2n + 6n2 = 0 Solving 9 + -2n + 6n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 1.5 + -0.3333333333n + n2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -0.3333333333n + -1.5 + n2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -0.3333333333n + n2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -0.3333333333n + n2 = 0 + -1.5 -0.3333333333n + n2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -0.3333333333n + n2 = -1.5 The n term is -0.3333333333n. Take half its coefficient (-0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. -0.3333333333n + 0.02777777779 + n2 = -1.5 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333n + n2 = -1.5 + 0.02777777779 Combine like terms: -1.5 + 0.02777777779 = -1.47222222221 0.02777777779 + -0.3333333333n + n2 = -1.47222222221 Factor a perfect square on the left side: (n + -0.1666666667)(n + -0.1666666667) = -1.47222222221 Can't calculate square root of the right side. The solution to this equation could not be determined.
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