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Simplifying n2 + 2n + -3 = 7 Reorder the terms: -3 + 2n + n2 = 7 Solving -3 + 2n + n2 = 7 Solving for variable 'n'. Reorder the terms: -3 + -7 + 2n + n2 = 7 + -7 Combine like terms: -3 + -7 = -10 -10 + 2n + n2 = 7 + -7 Combine like terms: 7 + -7 = 0 -10 + 2n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + 2n + 10 + n2 = 0 + 10 Reorder the terms: -10 + 10 + 2n + n2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 2n + n2 = 0 + 10 2n + n2 = 0 + 10 Combine like terms: 0 + 10 = 10 2n + n2 = 10 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 = 10 + 1 Reorder the terms: 1 + 2n + n2 = 10 + 1 Combine like terms: 10 + 1 = 11 1 + 2n + n2 = 11 Factor a perfect square on the left side: (n + 1)(n + 1) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (n + 1) equal to 3.31662479 and -3.31662479.Subproblem 1
n + 1 = 3.31662479 Simplifying n + 1 = 3.31662479 Reorder the terms: 1 + n = 3.31662479 Solving 1 + n = 3.31662479 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 = 3.31662479 + -1 Combine like terms: 1 + -1 = 0 0 + n = 3.31662479 + -1 n = 3.31662479 + -1 Combine like terms: 3.31662479 + -1 = 2.31662479 n = 2.31662479 Simplifying n = 2.31662479Subproblem 2
n + 1 = -3.31662479 Simplifying n + 1 = -3.31662479 Reorder the terms: 1 + n = -3.31662479 Solving 1 + n = -3.31662479 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 = -3.31662479 + -1 Combine like terms: 1 + -1 = 0 0 + n = -3.31662479 + -1 n = -3.31662479 + -1 Combine like terms: -3.31662479 + -1 = -4.31662479 n = -4.31662479 Simplifying n = -4.31662479Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.31662479, -4.31662479}
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