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Simplifying 5n2 + -17n + -6 = 0 Reorder the terms: -6 + -17n + 5n2 = 0 Solving -6 + -17n + 5n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.2 + -3.4n + n2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + -3.4n + 1.2 + n2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + -3.4n + n2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + -3.4n + n2 = 0 + 1.2 -3.4n + n2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 -3.4n + n2 = 1.2 The n term is -3.4n. Take half its coefficient (-1.7). Square it (2.89) and add it to both sides. Add '2.89' to each side of the equation. -3.4n + 2.89 + n2 = 1.2 + 2.89 Reorder the terms: 2.89 + -3.4n + n2 = 1.2 + 2.89 Combine like terms: 1.2 + 2.89 = 4.09 2.89 + -3.4n + n2 = 4.09 Factor a perfect square on the left side: (n + -1.7)(n + -1.7) = 4.09 Calculate the square root of the right side: 2.022374842 Break this problem into two subproblems by setting (n + -1.7) equal to 2.022374842 and -2.022374842.Subproblem 1
n + -1.7 = 2.022374842 Simplifying n + -1.7 = 2.022374842 Reorder the terms: -1.7 + n = 2.022374842 Solving -1.7 + n = 2.022374842 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.7' to each side of the equation. -1.7 + 1.7 + n = 2.022374842 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + n = 2.022374842 + 1.7 n = 2.022374842 + 1.7 Combine like terms: 2.022374842 + 1.7 = 3.722374842 n = 3.722374842 Simplifying n = 3.722374842Subproblem 2
n + -1.7 = -2.022374842 Simplifying n + -1.7 = -2.022374842 Reorder the terms: -1.7 + n = -2.022374842 Solving -1.7 + n = -2.022374842 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.7' to each side of the equation. -1.7 + 1.7 + n = -2.022374842 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + n = -2.022374842 + 1.7 n = -2.022374842 + 1.7 Combine like terms: -2.022374842 + 1.7 = -0.322374842 n = -0.322374842 Simplifying n = -0.322374842Solution
The solution to the problem is based on the solutions from the subproblems. n = {3.722374842, -0.322374842}
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