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Simplifying n2 + -4n + -74 = 0 Reorder the terms: -74 + -4n + n2 = 0 Solving -74 + -4n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '74' to each side of the equation. -74 + -4n + 74 + n2 = 0 + 74 Reorder the terms: -74 + 74 + -4n + n2 = 0 + 74 Combine like terms: -74 + 74 = 0 0 + -4n + n2 = 0 + 74 -4n + n2 = 0 + 74 Combine like terms: 0 + 74 = 74 -4n + n2 = 74 The n term is -4n. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4n + 4 + n2 = 74 + 4 Reorder the terms: 4 + -4n + n2 = 74 + 4 Combine like terms: 74 + 4 = 78 4 + -4n + n2 = 78 Factor a perfect square on the left side: (n + -2)(n + -2) = 78 Calculate the square root of the right side: 8.831760866 Break this problem into two subproblems by setting (n + -2) equal to 8.831760866 and -8.831760866.Subproblem 1
n + -2 = 8.831760866 Simplifying n + -2 = 8.831760866 Reorder the terms: -2 + n = 8.831760866 Solving -2 + n = 8.831760866 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + n = 8.831760866 + 2 Combine like terms: -2 + 2 = 0 0 + n = 8.831760866 + 2 n = 8.831760866 + 2 Combine like terms: 8.831760866 + 2 = 10.831760866 n = 10.831760866 Simplifying n = 10.831760866Subproblem 2
n + -2 = -8.831760866 Simplifying n + -2 = -8.831760866 Reorder the terms: -2 + n = -8.831760866 Solving -2 + n = -8.831760866 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + n = -8.831760866 + 2 Combine like terms: -2 + 2 = 0 0 + n = -8.831760866 + 2 n = -8.831760866 + 2 Combine like terms: -8.831760866 + 2 = -6.831760866 n = -6.831760866 Simplifying n = -6.831760866Solution
The solution to the problem is based on the solutions from the subproblems. n = {10.831760866, -6.831760866}
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