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Simplifying 9n2 + -2n + -15 = 0 Reorder the terms: -15 + -2n + 9n2 = 0 Solving -15 + -2n + 9n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.666666667 + -0.2222222222n + n2 = 0 Move the constant term to the right: Add '1.666666667' to each side of the equation. -1.666666667 + -0.2222222222n + 1.666666667 + n2 = 0 + 1.666666667 Reorder the terms: -1.666666667 + 1.666666667 + -0.2222222222n + n2 = 0 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + -0.2222222222n + n2 = 0 + 1.666666667 -0.2222222222n + n2 = 0 + 1.666666667 Combine like terms: 0 + 1.666666667 = 1.666666667 -0.2222222222n + n2 = 1.666666667 The n term is -0.2222222222n. Take half its coefficient (-0.1111111111). Square it (0.01234567901) and add it to both sides. Add '0.01234567901' to each side of the equation. -0.2222222222n + 0.01234567901 + n2 = 1.666666667 + 0.01234567901 Reorder the terms: 0.01234567901 + -0.2222222222n + n2 = 1.666666667 + 0.01234567901 Combine like terms: 1.666666667 + 0.01234567901 = 1.67901234601 0.01234567901 + -0.2222222222n + n2 = 1.67901234601 Factor a perfect square on the left side: (n + -0.1111111111)(n + -0.1111111111) = 1.67901234601 Calculate the square root of the right side: 1.295767088 Break this problem into two subproblems by setting (n + -0.1111111111) equal to 1.295767088 and -1.295767088.Subproblem 1
n + -0.1111111111 = 1.295767088 Simplifying n + -0.1111111111 = 1.295767088 Reorder the terms: -0.1111111111 + n = 1.295767088 Solving -0.1111111111 + n = 1.295767088 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.1111111111' to each side of the equation. -0.1111111111 + 0.1111111111 + n = 1.295767088 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + n = 1.295767088 + 0.1111111111 n = 1.295767088 + 0.1111111111 Combine like terms: 1.295767088 + 0.1111111111 = 1.4068781991 n = 1.4068781991 Simplifying n = 1.4068781991Subproblem 2
n + -0.1111111111 = -1.295767088 Simplifying n + -0.1111111111 = -1.295767088 Reorder the terms: -0.1111111111 + n = -1.295767088 Solving -0.1111111111 + n = -1.295767088 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.1111111111' to each side of the equation. -0.1111111111 + 0.1111111111 + n = -1.295767088 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + n = -1.295767088 + 0.1111111111 n = -1.295767088 + 0.1111111111 Combine like terms: -1.295767088 + 0.1111111111 = -1.1846559769 n = -1.1846559769 Simplifying n = -1.1846559769Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.4068781991, -1.1846559769}
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