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Simplifying 3n2 + -9n + -3 = 0 Reorder the terms: -3 + -9n + 3n2 = 0 Solving -3 + -9n + 3n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '3'. 3(-1 + -3n + n2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-1 + -3n + n2)' equal to zero and attempt to solve: Simplifying -1 + -3n + n2 = 0 Solving -1 + -3n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -3n + 1 + n2 = 0 + 1 Reorder the terms: -1 + 1 + -3n + n2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3n + n2 = 0 + 1 -3n + n2 = 0 + 1 Combine like terms: 0 + 1 = 1 -3n + n2 = 1 The n term is -3n. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3n + 2.25 + n2 = 1 + 2.25 Reorder the terms: 2.25 + -3n + n2 = 1 + 2.25 Combine like terms: 1 + 2.25 = 3.25 2.25 + -3n + n2 = 3.25 Factor a perfect square on the left side: (n + -1.5)(n + -1.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (n + -1.5) equal to 1.802775638 and -1.802775638.Subproblem 1
n + -1.5 = 1.802775638 Simplifying n + -1.5 = 1.802775638 Reorder the terms: -1.5 + n = 1.802775638 Solving -1.5 + n = 1.802775638 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + n = 1.802775638 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = 1.802775638 + 1.5 n = 1.802775638 + 1.5 Combine like terms: 1.802775638 + 1.5 = 3.302775638 n = 3.302775638 Simplifying n = 3.302775638Subproblem 2
n + -1.5 = -1.802775638 Simplifying n + -1.5 = -1.802775638 Reorder the terms: -1.5 + n = -1.802775638 Solving -1.5 + n = -1.802775638 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + n = -1.802775638 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = -1.802775638 + 1.5 n = -1.802775638 + 1.5 Combine like terms: -1.802775638 + 1.5 = -0.302775638 n = -0.302775638 Simplifying n = -0.302775638Solution
The solution to the problem is based on the solutions from the subproblems. n = {3.302775638, -0.302775638}Solution
n = {3.302775638, -0.302775638}
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