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Simplifying 4n2 + 5n + -159 = 0 Reorder the terms: -159 + 5n + 4n2 = 0 Solving -159 + 5n + 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'. -39.75 + 1.25n + n2 = 0 Move the constant term to the right: Add '39.75' to each side of the equation. -39.75 + 1.25n + 39.75 + n2 = 0 + 39.75 Reorder the terms: -39.75 + 39.75 + 1.25n + n2 = 0 + 39.75 Combine like terms: -39.75 + 39.75 = 0.00 0.00 + 1.25n + n2 = 0 + 39.75 1.25n + n2 = 0 + 39.75 Combine like terms: 0 + 39.75 = 39.75 1.25n + n2 = 39.75 The n term is 1.25n. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25n + 0.390625 + n2 = 39.75 + 0.390625 Reorder the terms: 0.390625 + 1.25n + n2 = 39.75 + 0.390625 Combine like terms: 39.75 + 0.390625 = 40.140625 0.390625 + 1.25n + n2 = 40.140625 Factor a perfect square on the left side: (n + 0.625)(n + 0.625) = 40.140625 Calculate the square root of the right side: 6.335662949 Break this problem into two subproblems by setting (n + 0.625) equal to 6.335662949 and -6.335662949.Subproblem 1
n + 0.625 = 6.335662949 Simplifying n + 0.625 = 6.335662949 Reorder the terms: 0.625 + n = 6.335662949 Solving 0.625 + n = 6.335662949 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + n = 6.335662949 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + n = 6.335662949 + -0.625 n = 6.335662949 + -0.625 Combine like terms: 6.335662949 + -0.625 = 5.710662949 n = 5.710662949 Simplifying n = 5.710662949Subproblem 2
n + 0.625 = -6.335662949 Simplifying n + 0.625 = -6.335662949 Reorder the terms: 0.625 + n = -6.335662949 Solving 0.625 + n = -6.335662949 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + n = -6.335662949 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + n = -6.335662949 + -0.625 n = -6.335662949 + -0.625 Combine like terms: -6.335662949 + -0.625 = -6.960662949 n = -6.960662949 Simplifying n = -6.960662949Solution
The solution to the problem is based on the solutions from the subproblems. n = {5.710662949, -6.960662949}
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