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Simplifying n2 + -3n + -50 = 0 Reorder the terms: -50 + -3n + n2 = 0 Solving -50 + -3n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '50' to each side of the equation. -50 + -3n + 50 + n2 = 0 + 50 Reorder the terms: -50 + 50 + -3n + n2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + -3n + n2 = 0 + 50 -3n + n2 = 0 + 50 Combine like terms: 0 + 50 = 50 -3n + n2 = 50 The n term is -3n. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3n + 2.25 + n2 = 50 + 2.25 Reorder the terms: 2.25 + -3n + n2 = 50 + 2.25 Combine like terms: 50 + 2.25 = 52.25 2.25 + -3n + n2 = 52.25 Factor a perfect square on the left side: (n + -1.5)(n + -1.5) = 52.25 Calculate the square root of the right side: 7.228416147 Break this problem into two subproblems by setting (n + -1.5) equal to 7.228416147 and -7.228416147.Subproblem 1
n + -1.5 = 7.228416147 Simplifying n + -1.5 = 7.228416147 Reorder the terms: -1.5 + n = 7.228416147 Solving -1.5 + n = 7.228416147 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + n = 7.228416147 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = 7.228416147 + 1.5 n = 7.228416147 + 1.5 Combine like terms: 7.228416147 + 1.5 = 8.728416147 n = 8.728416147 Simplifying n = 8.728416147Subproblem 2
n + -1.5 = -7.228416147 Simplifying n + -1.5 = -7.228416147 Reorder the terms: -1.5 + n = -7.228416147 Solving -1.5 + n = -7.228416147 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + n = -7.228416147 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = -7.228416147 + 1.5 n = -7.228416147 + 1.5 Combine like terms: -7.228416147 + 1.5 = -5.728416147 n = -5.728416147 Simplifying n = -5.728416147Solution
The solution to the problem is based on the solutions from the subproblems. n = {8.728416147, -5.728416147}
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