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Simplifying 3n2 + -9n + -9 = 0 Reorder the terms: -9 + -9n + 3n2 = 0 Solving -9 + -9n + 3n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '3'. 3(-3 + -3n + n2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-3 + -3n + n2)' equal to zero and attempt to solve: Simplifying -3 + -3n + n2 = 0 Solving -3 + -3n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -3n + 3 + n2 = 0 + 3 Reorder the terms: -3 + 3 + -3n + n2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -3n + n2 = 0 + 3 -3n + n2 = 0 + 3 Combine like terms: 0 + 3 = 3 -3n + n2 = 3 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 = 3 + 2.25 Reorder the terms: 2.25 + -3n + n2 = 3 + 2.25 Combine like terms: 3 + 2.25 = 5.25 2.25 + -3n + n2 = 5.25 Factor a perfect square on the left side: (n + -1.5)(n + -1.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (n + -1.5) equal to 2.291287847 and -2.291287847.Subproblem 1
n + -1.5 = 2.291287847 Simplifying n + -1.5 = 2.291287847 Reorder the terms: -1.5 + n = 2.291287847 Solving -1.5 + n = 2.291287847 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 = 2.291287847 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = 2.291287847 + 1.5 n = 2.291287847 + 1.5 Combine like terms: 2.291287847 + 1.5 = 3.791287847 n = 3.791287847 Simplifying n = 3.791287847Subproblem 2
n + -1.5 = -2.291287847 Simplifying n + -1.5 = -2.291287847 Reorder the terms: -1.5 + n = -2.291287847 Solving -1.5 + n = -2.291287847 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 = -2.291287847 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = -2.291287847 + 1.5 n = -2.291287847 + 1.5 Combine like terms: -2.291287847 + 1.5 = -0.791287847 n = -0.791287847 Simplifying n = -0.791287847Solution
The solution to the problem is based on the solutions from the subproblems. n = {3.791287847, -0.791287847}Solution
n = {3.791287847, -0.791287847}
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