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Simplifying 3n2 + -3n + -9 = 0 Reorder the terms: -9 + -3n + 3n2 = 0 Solving -9 + -3n + 3n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '3'. 3(-3 + -1n + n2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-3 + -1n + n2)' equal to zero and attempt to solve: Simplifying -3 + -1n + n2 = 0 Solving -3 + -1n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -1n + 3 + n2 = 0 + 3 Reorder the terms: -3 + 3 + -1n + n2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1n + n2 = 0 + 3 -1n + n2 = 0 + 3 Combine like terms: 0 + 3 = 3 -1n + n2 = 3 The n term is -1n. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1n + 0.25 + n2 = 3 + 0.25 Reorder the terms: 0.25 + -1n + n2 = 3 + 0.25 Combine like terms: 3 + 0.25 = 3.25 0.25 + -1n + n2 = 3.25 Factor a perfect square on the left side: (n + -0.5)(n + -0.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (n + -0.5) equal to 1.802775638 and -1.802775638.Subproblem 1
n + -0.5 = 1.802775638 Simplifying n + -0.5 = 1.802775638 Reorder the terms: -0.5 + n = 1.802775638 Solving -0.5 + n = 1.802775638 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + n = 1.802775638 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = 1.802775638 + 0.5 n = 1.802775638 + 0.5 Combine like terms: 1.802775638 + 0.5 = 2.302775638 n = 2.302775638 Simplifying n = 2.302775638Subproblem 2
n + -0.5 = -1.802775638 Simplifying n + -0.5 = -1.802775638 Reorder the terms: -0.5 + n = -1.802775638 Solving -0.5 + n = -1.802775638 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + n = -1.802775638 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = -1.802775638 + 0.5 n = -1.802775638 + 0.5 Combine like terms: -1.802775638 + 0.5 = -1.302775638 n = -1.302775638 Simplifying n = -1.302775638Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.302775638, -1.302775638}Solution
n = {2.302775638, -1.302775638}
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