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Simplifying -0.125n2 + 2n + -7 = 0 Reorder the terms: -7 + 2n + -0.125n2 = 0 Solving -7 + 2n + -0.125n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by -0.125 the coefficient of the squared term: Divide each side by '-0.125'. 56 + -16n + n2 = 0 Move the constant term to the right: Add '-56' to each side of the equation. 56 + -16n + -56 + n2 = 0 + -56 Reorder the terms: 56 + -56 + -16n + n2 = 0 + -56 Combine like terms: 56 + -56 = 0 0 + -16n + n2 = 0 + -56 -16n + n2 = 0 + -56 Combine like terms: 0 + -56 = -56 -16n + n2 = -56 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 = -56 + 64 Reorder the terms: 64 + -16n + n2 = -56 + 64 Combine like terms: -56 + 64 = 8 64 + -16n + n2 = 8 Factor a perfect square on the left side: (n + -8)(n + -8) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (n + -8) equal to 2.828427125 and -2.828427125.Subproblem 1
n + -8 = 2.828427125 Simplifying n + -8 = 2.828427125 Reorder the terms: -8 + n = 2.828427125 Solving -8 + n = 2.828427125 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 = 2.828427125 + 8 Combine like terms: -8 + 8 = 0 0 + n = 2.828427125 + 8 n = 2.828427125 + 8 Combine like terms: 2.828427125 + 8 = 10.828427125 n = 10.828427125 Simplifying n = 10.828427125Subproblem 2
n + -8 = -2.828427125 Simplifying n + -8 = -2.828427125 Reorder the terms: -8 + n = -2.828427125 Solving -8 + n = -2.828427125 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 = -2.828427125 + 8 Combine like terms: -8 + 8 = 0 0 + n = -2.828427125 + 8 n = -2.828427125 + 8 Combine like terms: -2.828427125 + 8 = 5.171572875 n = 5.171572875 Simplifying n = 5.171572875Solution
The solution to the problem is based on the solutions from the subproblems. n = {10.828427125, 5.171572875}
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