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Simplifying n2 + -1n + -10 = -1 Reorder the terms: -10 + -1n + n2 = -1 Solving -10 + -1n + n2 = -1 Solving for variable 'n'. Reorder the terms: -10 + 1 + -1n + n2 = -1 + 1 Combine like terms: -10 + 1 = -9 -9 + -1n + n2 = -1 + 1 Combine like terms: -1 + 1 = 0 -9 + -1n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -1n + 9 + n2 = 0 + 9 Reorder the terms: -9 + 9 + -1n + n2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1n + n2 = 0 + 9 -1n + n2 = 0 + 9 Combine like terms: 0 + 9 = 9 -1n + n2 = 9 The n term is -1n. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1n + 0.25 + n2 = 9 + 0.25 Reorder the terms: 0.25 + -1n + n2 = 9 + 0.25 Combine like terms: 9 + 0.25 = 9.25 0.25 + -1n + n2 = 9.25 Factor a perfect square on the left side: (n + -0.5)(n + -0.5) = 9.25 Calculate the square root of the right side: 3.041381265 Break this problem into two subproblems by setting (n + -0.5) equal to 3.041381265 and -3.041381265.Subproblem 1
n + -0.5 = 3.041381265 Simplifying n + -0.5 = 3.041381265 Reorder the terms: -0.5 + n = 3.041381265 Solving -0.5 + n = 3.041381265 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + n = 3.041381265 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = 3.041381265 + 0.5 n = 3.041381265 + 0.5 Combine like terms: 3.041381265 + 0.5 = 3.541381265 n = 3.541381265 Simplifying n = 3.541381265Subproblem 2
n + -0.5 = -3.041381265 Simplifying n + -0.5 = -3.041381265 Reorder the terms: -0.5 + n = -3.041381265 Solving -0.5 + n = -3.041381265 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + n = -3.041381265 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = -3.041381265 + 0.5 n = -3.041381265 + 0.5 Combine like terms: -3.041381265 + 0.5 = -2.541381265 n = -2.541381265 Simplifying n = -2.541381265Solution
The solution to the problem is based on the solutions from the subproblems. n = {3.541381265, -2.541381265}
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