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Simplifying n2 + -16n + 2 = -4 Reorder the terms: 2 + -16n + n2 = -4 Solving 2 + -16n + n2 = -4 Solving for variable 'n'. Reorder the terms: 2 + 4 + -16n + n2 = -4 + 4 Combine like terms: 2 + 4 = 6 6 + -16n + n2 = -4 + 4 Combine like terms: -4 + 4 = 0 6 + -16n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + -16n + -6 + n2 = 0 + -6 Reorder the terms: 6 + -6 + -16n + n2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -16n + n2 = 0 + -6 -16n + n2 = 0 + -6 Combine like terms: 0 + -6 = -6 -16n + n2 = -6 The n term is -16n. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16n + 64 + n2 = -6 + 64 Reorder the terms: 64 + -16n + n2 = -6 + 64 Combine like terms: -6 + 64 = 58 64 + -16n + n2 = 58 Factor a perfect square on the left side: (n + -8)(n + -8) = 58 Calculate the square root of the right side: 7.615773106 Break this problem into two subproblems by setting (n + -8) equal to 7.615773106 and -7.615773106.Subproblem 1
n + -8 = 7.615773106 Simplifying n + -8 = 7.615773106 Reorder the terms: -8 + n = 7.615773106 Solving -8 + n = 7.615773106 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + n = 7.615773106 + 8 Combine like terms: -8 + 8 = 0 0 + n = 7.615773106 + 8 n = 7.615773106 + 8 Combine like terms: 7.615773106 + 8 = 15.615773106 n = 15.615773106 Simplifying n = 15.615773106Subproblem 2
n + -8 = -7.615773106 Simplifying n + -8 = -7.615773106 Reorder the terms: -8 + n = -7.615773106 Solving -8 + n = -7.615773106 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + n = -7.615773106 + 8 Combine like terms: -8 + 8 = 0 0 + n = -7.615773106 + 8 n = -7.615773106 + 8 Combine like terms: -7.615773106 + 8 = 0.384226894 n = 0.384226894 Simplifying n = 0.384226894Solution
The solution to the problem is based on the solutions from the subproblems. n = {15.615773106, 0.384226894}
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