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Simplifying 7n2 + -14n + -49 = 70 Reorder the terms: -49 + -14n + 7n2 = 70 Solving -49 + -14n + 7n2 = 70 Solving for variable 'n'. Reorder the terms: -49 + -70 + -14n + 7n2 = 70 + -70 Combine like terms: -49 + -70 = -119 -119 + -14n + 7n2 = 70 + -70 Combine like terms: 70 + -70 = 0 -119 + -14n + 7n2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(-17 + -2n + n2) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(-17 + -2n + n2)' equal to zero and attempt to solve: Simplifying -17 + -2n + n2 = 0 Solving -17 + -2n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '17' to each side of the equation. -17 + -2n + 17 + n2 = 0 + 17 Reorder the terms: -17 + 17 + -2n + n2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + -2n + n2 = 0 + 17 -2n + n2 = 0 + 17 Combine like terms: 0 + 17 = 17 -2n + n2 = 17 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 = 17 + 1 Reorder the terms: 1 + -2n + n2 = 17 + 1 Combine like terms: 17 + 1 = 18 1 + -2n + n2 = 18 Factor a perfect square on the left side: (n + -1)(n + -1) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (n + -1) equal to 4.242640687 and -4.242640687.Subproblem 1
n + -1 = 4.242640687 Simplifying n + -1 = 4.242640687 Reorder the terms: -1 + n = 4.242640687 Solving -1 + n = 4.242640687 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 = 4.242640687 + 1 Combine like terms: -1 + 1 = 0 0 + n = 4.242640687 + 1 n = 4.242640687 + 1 Combine like terms: 4.242640687 + 1 = 5.242640687 n = 5.242640687 Simplifying n = 5.242640687Subproblem 2
n + -1 = -4.242640687 Simplifying n + -1 = -4.242640687 Reorder the terms: -1 + n = -4.242640687 Solving -1 + n = -4.242640687 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 = -4.242640687 + 1 Combine like terms: -1 + 1 = 0 0 + n = -4.242640687 + 1 n = -4.242640687 + 1 Combine like terms: -4.242640687 + 1 = -3.242640687 n = -3.242640687 Simplifying n = -3.242640687Solution
The solution to the problem is based on the solutions from the subproblems. n = {5.242640687, -3.242640687}Solution
n = {5.242640687, -3.242640687}
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