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Simplifying n2 + -2n + -1 = 154 Reorder the terms: -1 + -2n + n2 = 154 Solving -1 + -2n + n2 = 154 Solving for variable 'n'. Reorder the terms: -1 + -154 + -2n + n2 = 154 + -154 Combine like terms: -1 + -154 = -155 -155 + -2n + n2 = 154 + -154 Combine like terms: 154 + -154 = 0 -155 + -2n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '155' to each side of the equation. -155 + -2n + 155 + n2 = 0 + 155 Reorder the terms: -155 + 155 + -2n + n2 = 0 + 155 Combine like terms: -155 + 155 = 0 0 + -2n + n2 = 0 + 155 -2n + n2 = 0 + 155 Combine like terms: 0 + 155 = 155 -2n + n2 = 155 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 = 155 + 1 Reorder the terms: 1 + -2n + n2 = 155 + 1 Combine like terms: 155 + 1 = 156 1 + -2n + n2 = 156 Factor a perfect square on the left side: (n + -1)(n + -1) = 156 Calculate the square root of the right side: 12.489995997 Break this problem into two subproblems by setting (n + -1) equal to 12.489995997 and -12.489995997.Subproblem 1
n + -1 = 12.489995997 Simplifying n + -1 = 12.489995997 Reorder the terms: -1 + n = 12.489995997 Solving -1 + n = 12.489995997 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 = 12.489995997 + 1 Combine like terms: -1 + 1 = 0 0 + n = 12.489995997 + 1 n = 12.489995997 + 1 Combine like terms: 12.489995997 + 1 = 13.489995997 n = 13.489995997 Simplifying n = 13.489995997Subproblem 2
n + -1 = -12.489995997 Simplifying n + -1 = -12.489995997 Reorder the terms: -1 + n = -12.489995997 Solving -1 + n = -12.489995997 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 = -12.489995997 + 1 Combine like terms: -1 + 1 = 0 0 + n = -12.489995997 + 1 n = -12.489995997 + 1 Combine like terms: -12.489995997 + 1 = -11.489995997 n = -11.489995997 Simplifying n = -11.489995997Solution
The solution to the problem is based on the solutions from the subproblems. n = {13.489995997, -11.489995997}
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