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Simplifying 7n + -2 = 7n2 + -5n + 6 Reorder the terms: -2 + 7n = 7n2 + -5n + 6 Reorder the terms: -2 + 7n = 6 + -5n + 7n2 Solving -2 + 7n = 6 + -5n + 7n2 Solving for variable 'n'. Reorder the terms: -2 + -6 + 7n + 5n + -7n2 = 6 + -5n + 7n2 + -6 + 5n + -7n2 Combine like terms: -2 + -6 = -8 -8 + 7n + 5n + -7n2 = 6 + -5n + 7n2 + -6 + 5n + -7n2 Combine like terms: 7n + 5n = 12n -8 + 12n + -7n2 = 6 + -5n + 7n2 + -6 + 5n + -7n2 Reorder the terms: -8 + 12n + -7n2 = 6 + -6 + -5n + 5n + 7n2 + -7n2 Combine like terms: 6 + -6 = 0 -8 + 12n + -7n2 = 0 + -5n + 5n + 7n2 + -7n2 -8 + 12n + -7n2 = -5n + 5n + 7n2 + -7n2 Combine like terms: -5n + 5n = 0 -8 + 12n + -7n2 = 0 + 7n2 + -7n2 -8 + 12n + -7n2 = 7n2 + -7n2 Combine like terms: 7n2 + -7n2 = 0 -8 + 12n + -7n2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. 1.142857143 + -1.714285714n + n2 = 0 Move the constant term to the right: Add '-1.142857143' to each side of the equation. 1.142857143 + -1.714285714n + -1.142857143 + n2 = 0 + -1.142857143 Reorder the terms: 1.142857143 + -1.142857143 + -1.714285714n + n2 = 0 + -1.142857143 Combine like terms: 1.142857143 + -1.142857143 = 0.000000000 0.000000000 + -1.714285714n + n2 = 0 + -1.142857143 -1.714285714n + n2 = 0 + -1.142857143 Combine like terms: 0 + -1.142857143 = -1.142857143 -1.714285714n + n2 = -1.142857143 The n term is -1.714285714n. Take half its coefficient (-0.857142857). Square it (0.7346938773) and add it to both sides. Add '0.7346938773' to each side of the equation. -1.714285714n + 0.7346938773 + n2 = -1.142857143 + 0.7346938773 Reorder the terms: 0.7346938773 + -1.714285714n + n2 = -1.142857143 + 0.7346938773 Combine like terms: -1.142857143 + 0.7346938773 = -0.4081632657 0.7346938773 + -1.714285714n + n2 = -0.4081632657 Factor a perfect square on the left side: (n + -0.857142857)(n + -0.857142857) = -0.4081632657 Can't calculate square root of the right side. The solution to this equation could not be determined.
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