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Simplifying 4n2 + -17n + -4 = 0 Reorder the terms: -4 + -17n + 4n2 = 0 Solving -4 + -17n + 4n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1 + -4.25n + n2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -4.25n + 1 + n2 = 0 + 1 Reorder the terms: -1 + 1 + -4.25n + n2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -4.25n + n2 = 0 + 1 -4.25n + n2 = 0 + 1 Combine like terms: 0 + 1 = 1 -4.25n + n2 = 1 The n term is -4.25n. Take half its coefficient (-2.125). Square it (4.515625) and add it to both sides. Add '4.515625' to each side of the equation. -4.25n + 4.515625 + n2 = 1 + 4.515625 Reorder the terms: 4.515625 + -4.25n + n2 = 1 + 4.515625 Combine like terms: 1 + 4.515625 = 5.515625 4.515625 + -4.25n + n2 = 5.515625 Factor a perfect square on the left side: (n + -2.125)(n + -2.125) = 5.515625 Calculate the square root of the right side: 2.348536779 Break this problem into two subproblems by setting (n + -2.125) equal to 2.348536779 and -2.348536779.Subproblem 1
n + -2.125 = 2.348536779 Simplifying n + -2.125 = 2.348536779 Reorder the terms: -2.125 + n = 2.348536779 Solving -2.125 + n = 2.348536779 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2.125' to each side of the equation. -2.125 + 2.125 + n = 2.348536779 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + n = 2.348536779 + 2.125 n = 2.348536779 + 2.125 Combine like terms: 2.348536779 + 2.125 = 4.473536779 n = 4.473536779 Simplifying n = 4.473536779Subproblem 2
n + -2.125 = -2.348536779 Simplifying n + -2.125 = -2.348536779 Reorder the terms: -2.125 + n = -2.348536779 Solving -2.125 + n = -2.348536779 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2.125' to each side of the equation. -2.125 + 2.125 + n = -2.348536779 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + n = -2.348536779 + 2.125 n = -2.348536779 + 2.125 Combine like terms: -2.348536779 + 2.125 = -0.223536779 n = -0.223536779 Simplifying n = -0.223536779Solution
The solution to the problem is based on the solutions from the subproblems. n = {4.473536779, -0.223536779}
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