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Simplifying n2 + -3n + -10 = n + 5 Reorder the terms: -10 + -3n + n2 = n + 5 Reorder the terms: -10 + -3n + n2 = 5 + n Solving -10 + -3n + n2 = 5 + n Solving for variable 'n'. Reorder the terms: -10 + -5 + -3n + -1n + n2 = 5 + n + -5 + -1n Combine like terms: -10 + -5 = -15 -15 + -3n + -1n + n2 = 5 + n + -5 + -1n Combine like terms: -3n + -1n = -4n -15 + -4n + n2 = 5 + n + -5 + -1n Reorder the terms: -15 + -4n + n2 = 5 + -5 + n + -1n Combine like terms: 5 + -5 = 0 -15 + -4n + n2 = 0 + n + -1n -15 + -4n + n2 = n + -1n Combine like terms: n + -1n = 0 -15 + -4n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + -4n + 15 + n2 = 0 + 15 Reorder the terms: -15 + 15 + -4n + n2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -4n + n2 = 0 + 15 -4n + n2 = 0 + 15 Combine like terms: 0 + 15 = 15 -4n + n2 = 15 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 = 15 + 4 Reorder the terms: 4 + -4n + n2 = 15 + 4 Combine like terms: 15 + 4 = 19 4 + -4n + n2 = 19 Factor a perfect square on the left side: (n + -2)(n + -2) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (n + -2) equal to 4.358898944 and -4.358898944.Subproblem 1
n + -2 = 4.358898944 Simplifying n + -2 = 4.358898944 Reorder the terms: -2 + n = 4.358898944 Solving -2 + n = 4.358898944 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 = 4.358898944 + 2 Combine like terms: -2 + 2 = 0 0 + n = 4.358898944 + 2 n = 4.358898944 + 2 Combine like terms: 4.358898944 + 2 = 6.358898944 n = 6.358898944 Simplifying n = 6.358898944Subproblem 2
n + -2 = -4.358898944 Simplifying n + -2 = -4.358898944 Reorder the terms: -2 + n = -4.358898944 Solving -2 + n = -4.358898944 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 = -4.358898944 + 2 Combine like terms: -2 + 2 = 0 0 + n = -4.358898944 + 2 n = -4.358898944 + 2 Combine like terms: -4.358898944 + 2 = -2.358898944 n = -2.358898944 Simplifying n = -2.358898944Solution
The solution to the problem is based on the solutions from the subproblems. n = {6.358898944, -2.358898944}
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