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Simplifying 7n2 + 56n + 14 = 0 Reorder the terms: 14 + 56n + 7n2 = 0 Solving 14 + 56n + 7n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '7'. 7(2 + 8n + n2) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(2 + 8n + n2)' equal to zero and attempt to solve: Simplifying 2 + 8n + n2 = 0 Solving 2 + 8n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + 8n + -2 + n2 = 0 + -2 Reorder the terms: 2 + -2 + 8n + n2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 8n + n2 = 0 + -2 8n + n2 = 0 + -2 Combine like terms: 0 + -2 = -2 8n + n2 = -2 The n term is 8n. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8n + 16 + n2 = -2 + 16 Reorder the terms: 16 + 8n + n2 = -2 + 16 Combine like terms: -2 + 16 = 14 16 + 8n + n2 = 14 Factor a perfect square on the left side: (n + 4)(n + 4) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (n + 4) equal to 3.741657387 and -3.741657387.Subproblem 1
n + 4 = 3.741657387 Simplifying n + 4 = 3.741657387 Reorder the terms: 4 + n = 3.741657387 Solving 4 + n = 3.741657387 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + n = 3.741657387 + -4 Combine like terms: 4 + -4 = 0 0 + n = 3.741657387 + -4 n = 3.741657387 + -4 Combine like terms: 3.741657387 + -4 = -0.258342613 n = -0.258342613 Simplifying n = -0.258342613Subproblem 2
n + 4 = -3.741657387 Simplifying n + 4 = -3.741657387 Reorder the terms: 4 + n = -3.741657387 Solving 4 + n = -3.741657387 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + n = -3.741657387 + -4 Combine like terms: 4 + -4 = 0 0 + n = -3.741657387 + -4 n = -3.741657387 + -4 Combine like terms: -3.741657387 + -4 = -7.741657387 n = -7.741657387 Simplifying n = -7.741657387Solution
The solution to the problem is based on the solutions from the subproblems. n = {-0.258342613, -7.741657387}Solution
n = {-0.258342613, -7.741657387}
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