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Simplifying -3n2 + -44n + 225 = 0 Reorder the terms: 225 + -44n + -3n2 = 0 Solving 225 + -44n + -3n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -75 + 14.66666667n + n2 = 0 Move the constant term to the right: Add '75' to each side of the equation. -75 + 14.66666667n + 75 + n2 = 0 + 75 Reorder the terms: -75 + 75 + 14.66666667n + n2 = 0 + 75 Combine like terms: -75 + 75 = 0 0 + 14.66666667n + n2 = 0 + 75 14.66666667n + n2 = 0 + 75 Combine like terms: 0 + 75 = 75 14.66666667n + n2 = 75 The n term is 14.66666667n. Take half its coefficient (7.333333335). Square it (53.77777780) and add it to both sides. Add '53.77777780' to each side of the equation. 14.66666667n + 53.77777780 + n2 = 75 + 53.77777780 Reorder the terms: 53.77777780 + 14.66666667n + n2 = 75 + 53.77777780 Combine like terms: 75 + 53.77777780 = 128.7777778 53.77777780 + 14.66666667n + n2 = 128.7777778 Factor a perfect square on the left side: (n + 7.333333335)(n + 7.333333335) = 128.7777778 Calculate the square root of the right side: 11.348029688 Break this problem into two subproblems by setting (n + 7.333333335) equal to 11.348029688 and -11.348029688.Subproblem 1
n + 7.333333335 = 11.348029688 Simplifying n + 7.333333335 = 11.348029688 Reorder the terms: 7.333333335 + n = 11.348029688 Solving 7.333333335 + n = 11.348029688 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-7.333333335' to each side of the equation. 7.333333335 + -7.333333335 + n = 11.348029688 + -7.333333335 Combine like terms: 7.333333335 + -7.333333335 = 0.000000000 0.000000000 + n = 11.348029688 + -7.333333335 n = 11.348029688 + -7.333333335 Combine like terms: 11.348029688 + -7.333333335 = 4.014696353 n = 4.014696353 Simplifying n = 4.014696353Subproblem 2
n + 7.333333335 = -11.348029688 Simplifying n + 7.333333335 = -11.348029688 Reorder the terms: 7.333333335 + n = -11.348029688 Solving 7.333333335 + n = -11.348029688 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-7.333333335' to each side of the equation. 7.333333335 + -7.333333335 + n = -11.348029688 + -7.333333335 Combine like terms: 7.333333335 + -7.333333335 = 0.000000000 0.000000000 + n = -11.348029688 + -7.333333335 n = -11.348029688 + -7.333333335 Combine like terms: -11.348029688 + -7.333333335 = -18.681363023 n = -18.681363023 Simplifying n = -18.681363023Solution
The solution to the problem is based on the solutions from the subproblems. n = {4.014696353, -18.681363023}
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