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Simplifying 4n2 + -15n + -36 = 0 Reorder the terms: -36 + -15n + 4n2 = 0 Solving -36 + -15n + 4n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -9 + -3.75n + n2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + -3.75n + 9 + n2 = 0 + 9 Reorder the terms: -9 + 9 + -3.75n + n2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -3.75n + n2 = 0 + 9 -3.75n + n2 = 0 + 9 Combine like terms: 0 + 9 = 9 -3.75n + n2 = 9 The n term is -3.75n. Take half its coefficient (-1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. -3.75n + 3.515625 + n2 = 9 + 3.515625 Reorder the terms: 3.515625 + -3.75n + n2 = 9 + 3.515625 Combine like terms: 9 + 3.515625 = 12.515625 3.515625 + -3.75n + n2 = 12.515625 Factor a perfect square on the left side: (n + -1.875)(n + -1.875) = 12.515625 Calculate the square root of the right side: 3.537742925 Break this problem into two subproblems by setting (n + -1.875) equal to 3.537742925 and -3.537742925.Subproblem 1
n + -1.875 = 3.537742925 Simplifying n + -1.875 = 3.537742925 Reorder the terms: -1.875 + n = 3.537742925 Solving -1.875 + n = 3.537742925 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + n = 3.537742925 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + n = 3.537742925 + 1.875 n = 3.537742925 + 1.875 Combine like terms: 3.537742925 + 1.875 = 5.412742925 n = 5.412742925 Simplifying n = 5.412742925Subproblem 2
n + -1.875 = -3.537742925 Simplifying n + -1.875 = -3.537742925 Reorder the terms: -1.875 + n = -3.537742925 Solving -1.875 + n = -3.537742925 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + n = -3.537742925 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + n = -3.537742925 + 1.875 n = -3.537742925 + 1.875 Combine like terms: -3.537742925 + 1.875 = -1.662742925 n = -1.662742925 Simplifying n = -1.662742925Solution
The solution to the problem is based on the solutions from the subproblems. n = {5.412742925, -1.662742925}
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