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Simplifying n2 + 6n + -9 = 6 Reorder the terms: -9 + 6n + n2 = 6 Solving -9 + 6n + n2 = 6 Solving for variable 'n'. Reorder the terms: -9 + -6 + 6n + n2 = 6 + -6 Combine like terms: -9 + -6 = -15 -15 + 6n + n2 = 6 + -6 Combine like terms: 6 + -6 = 0 -15 + 6n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + 6n + 15 + n2 = 0 + 15 Reorder the terms: -15 + 15 + 6n + n2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 6n + n2 = 0 + 15 6n + n2 = 0 + 15 Combine like terms: 0 + 15 = 15 6n + n2 = 15 The n term is 6n. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6n + 9 + n2 = 15 + 9 Reorder the terms: 9 + 6n + n2 = 15 + 9 Combine like terms: 15 + 9 = 24 9 + 6n + n2 = 24 Factor a perfect square on the left side: (n + 3)(n + 3) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (n + 3) equal to 4.898979486 and -4.898979486.Subproblem 1
n + 3 = 4.898979486 Simplifying n + 3 = 4.898979486 Reorder the terms: 3 + n = 4.898979486 Solving 3 + n = 4.898979486 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + n = 4.898979486 + -3 Combine like terms: 3 + -3 = 0 0 + n = 4.898979486 + -3 n = 4.898979486 + -3 Combine like terms: 4.898979486 + -3 = 1.898979486 n = 1.898979486 Simplifying n = 1.898979486Subproblem 2
n + 3 = -4.898979486 Simplifying n + 3 = -4.898979486 Reorder the terms: 3 + n = -4.898979486 Solving 3 + n = -4.898979486 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + n = -4.898979486 + -3 Combine like terms: 3 + -3 = 0 0 + n = -4.898979486 + -3 n = -4.898979486 + -3 Combine like terms: -4.898979486 + -3 = -7.898979486 n = -7.898979486 Simplifying n = -7.898979486Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.898979486, -7.898979486}
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