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Simplifying 4n2 + -17n + 5 = 0 Reorder the terms: 5 + -17n + 4n2 = 0 Solving 5 + -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'. 1.25 + -4.25n + n2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + -4.25n + -1.25 + n2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + -4.25n + n2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + -4.25n + n2 = 0 + -1.25 -4.25n + n2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 -4.25n + n2 = -1.25 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 = -1.25 + 4.515625 Reorder the terms: 4.515625 + -4.25n + n2 = -1.25 + 4.515625 Combine like terms: -1.25 + 4.515625 = 3.265625 4.515625 + -4.25n + n2 = 3.265625 Factor a perfect square on the left side: (n + -2.125)(n + -2.125) = 3.265625 Calculate the square root of the right side: 1.807104037 Break this problem into two subproblems by setting (n + -2.125) equal to 1.807104037 and -1.807104037.Subproblem 1
n + -2.125 = 1.807104037 Simplifying n + -2.125 = 1.807104037 Reorder the terms: -2.125 + n = 1.807104037 Solving -2.125 + n = 1.807104037 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 = 1.807104037 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + n = 1.807104037 + 2.125 n = 1.807104037 + 2.125 Combine like terms: 1.807104037 + 2.125 = 3.932104037 n = 3.932104037 Simplifying n = 3.932104037Subproblem 2
n + -2.125 = -1.807104037 Simplifying n + -2.125 = -1.807104037 Reorder the terms: -2.125 + n = -1.807104037 Solving -2.125 + n = -1.807104037 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 = -1.807104037 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + n = -1.807104037 + 2.125 n = -1.807104037 + 2.125 Combine like terms: -1.807104037 + 2.125 = 0.317895963 n = 0.317895963 Simplifying n = 0.317895963Solution
The solution to the problem is based on the solutions from the subproblems. n = {3.932104037, 0.317895963}
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