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Simplifying n2 + -2n + -70 = 0 Reorder the terms: -70 + -2n + n2 = 0 Solving -70 + -2n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '70' to each side of the equation. -70 + -2n + 70 + n2 = 0 + 70 Reorder the terms: -70 + 70 + -2n + n2 = 0 + 70 Combine like terms: -70 + 70 = 0 0 + -2n + n2 = 0 + 70 -2n + n2 = 0 + 70 Combine like terms: 0 + 70 = 70 -2n + n2 = 70 The n term is -2n. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2n + 1 + n2 = 70 + 1 Reorder the terms: 1 + -2n + n2 = 70 + 1 Combine like terms: 70 + 1 = 71 1 + -2n + n2 = 71 Factor a perfect square on the left side: (n + -1)(n + -1) = 71 Calculate the square root of the right side: 8.426149773 Break this problem into two subproblems by setting (n + -1) equal to 8.426149773 and -8.426149773.Subproblem 1
n + -1 = 8.426149773 Simplifying n + -1 = 8.426149773 Reorder the terms: -1 + n = 8.426149773 Solving -1 + n = 8.426149773 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + n = 8.426149773 + 1 Combine like terms: -1 + 1 = 0 0 + n = 8.426149773 + 1 n = 8.426149773 + 1 Combine like terms: 8.426149773 + 1 = 9.426149773 n = 9.426149773 Simplifying n = 9.426149773Subproblem 2
n + -1 = -8.426149773 Simplifying n + -1 = -8.426149773 Reorder the terms: -1 + n = -8.426149773 Solving -1 + n = -8.426149773 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + n = -8.426149773 + 1 Combine like terms: -1 + 1 = 0 0 + n = -8.426149773 + 1 n = -8.426149773 + 1 Combine like terms: -8.426149773 + 1 = -7.426149773 n = -7.426149773 Simplifying n = -7.426149773Solution
The solution to the problem is based on the solutions from the subproblems. n = {9.426149773, -7.426149773}
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