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Simplifying 4n2 + -9n + -5 = 0 Reorder the terms: -5 + -9n + 4n2 = 0 Solving -5 + -9n + 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 + -2.25n + n2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -2.25n + 1.25 + n2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -2.25n + n2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -2.25n + n2 = 0 + 1.25 -2.25n + n2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -2.25n + n2 = 1.25 The n term is -2.25n. Take half its coefficient (-1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. -2.25n + 1.265625 + n2 = 1.25 + 1.265625 Reorder the terms: 1.265625 + -2.25n + n2 = 1.25 + 1.265625 Combine like terms: 1.25 + 1.265625 = 2.515625 1.265625 + -2.25n + n2 = 2.515625 Factor a perfect square on the left side: (n + -1.125)(n + -1.125) = 2.515625 Calculate the square root of the right side: 1.586072193 Break this problem into two subproblems by setting (n + -1.125) equal to 1.586072193 and -1.586072193.Subproblem 1
n + -1.125 = 1.586072193 Simplifying n + -1.125 = 1.586072193 Reorder the terms: -1.125 + n = 1.586072193 Solving -1.125 + n = 1.586072193 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + n = 1.586072193 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + n = 1.586072193 + 1.125 n = 1.586072193 + 1.125 Combine like terms: 1.586072193 + 1.125 = 2.711072193 n = 2.711072193 Simplifying n = 2.711072193Subproblem 2
n + -1.125 = -1.586072193 Simplifying n + -1.125 = -1.586072193 Reorder the terms: -1.125 + n = -1.586072193 Solving -1.125 + n = -1.586072193 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + n = -1.586072193 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + n = -1.586072193 + 1.125 n = -1.586072193 + 1.125 Combine like terms: -1.586072193 + 1.125 = -0.461072193 n = -0.461072193 Simplifying n = -0.461072193Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.711072193, -0.461072193}
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