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Simplifying 2n2 + -12n + -10 = 0 Reorder the terms: -10 + -12n + 2n2 = 0 Solving -10 + -12n + 2n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + -6n + n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -6n + n2)' equal to zero and attempt to solve: Simplifying -5 + -6n + n2 = 0 Solving -5 + -6n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -6n + 5 + n2 = 0 + 5 Reorder the terms: -5 + 5 + -6n + n2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -6n + n2 = 0 + 5 -6n + n2 = 0 + 5 Combine like terms: 0 + 5 = 5 -6n + n2 = 5 The n term is -6n. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6n + 9 + n2 = 5 + 9 Reorder the terms: 9 + -6n + n2 = 5 + 9 Combine like terms: 5 + 9 = 14 9 + -6n + n2 = 14 Factor a perfect square on the left side: (n + -3)(n + -3) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (n + -3) equal to 3.741657387 and -3.741657387.Subproblem 1
n + -3 = 3.741657387 Simplifying n + -3 = 3.741657387 Reorder the terms: -3 + n = 3.741657387 Solving -3 + n = 3.741657387 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + n = 3.741657387 + 3 Combine like terms: -3 + 3 = 0 0 + n = 3.741657387 + 3 n = 3.741657387 + 3 Combine like terms: 3.741657387 + 3 = 6.741657387 n = 6.741657387 Simplifying n = 6.741657387Subproblem 2
n + -3 = -3.741657387 Simplifying n + -3 = -3.741657387 Reorder the terms: -3 + n = -3.741657387 Solving -3 + n = -3.741657387 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + n = -3.741657387 + 3 Combine like terms: -3 + 3 = 0 0 + n = -3.741657387 + 3 n = -3.741657387 + 3 Combine like terms: -3.741657387 + 3 = -0.741657387 n = -0.741657387 Simplifying n = -0.741657387Solution
The solution to the problem is based on the solutions from the subproblems. n = {6.741657387, -0.741657387}Solution
n = {6.741657387, -0.741657387}
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