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Simplifying 3n2 = -12n + 21 Reorder the terms: 3n2 = 21 + -12n Solving 3n2 = 21 + -12n Solving for variable 'n'. Reorder the terms: -21 + 12n + 3n2 = 21 + -12n + -21 + 12n Reorder the terms: -21 + 12n + 3n2 = 21 + -21 + -12n + 12n Combine like terms: 21 + -21 = 0 -21 + 12n + 3n2 = 0 + -12n + 12n -21 + 12n + 3n2 = -12n + 12n Combine like terms: -12n + 12n = 0 -21 + 12n + 3n2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-7 + 4n + n2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-7 + 4n + n2)' equal to zero and attempt to solve: Simplifying -7 + 4n + n2 = 0 Solving -7 + 4n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + 4n + 7 + n2 = 0 + 7 Reorder the terms: -7 + 7 + 4n + n2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 4n + n2 = 0 + 7 4n + n2 = 0 + 7 Combine like terms: 0 + 7 = 7 4n + n2 = 7 The n term is 4n. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4n + 4 + n2 = 7 + 4 Reorder the terms: 4 + 4n + n2 = 7 + 4 Combine like terms: 7 + 4 = 11 4 + 4n + n2 = 11 Factor a perfect square on the left side: (n + 2)(n + 2) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (n + 2) equal to 3.31662479 and -3.31662479.Subproblem 1
n + 2 = 3.31662479 Simplifying n + 2 = 3.31662479 Reorder the terms: 2 + n = 3.31662479 Solving 2 + n = 3.31662479 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + n = 3.31662479 + -2 Combine like terms: 2 + -2 = 0 0 + n = 3.31662479 + -2 n = 3.31662479 + -2 Combine like terms: 3.31662479 + -2 = 1.31662479 n = 1.31662479 Simplifying n = 1.31662479Subproblem 2
n + 2 = -3.31662479 Simplifying n + 2 = -3.31662479 Reorder the terms: 2 + n = -3.31662479 Solving 2 + n = -3.31662479 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + n = -3.31662479 + -2 Combine like terms: 2 + -2 = 0 0 + n = -3.31662479 + -2 n = -3.31662479 + -2 Combine like terms: -3.31662479 + -2 = -5.31662479 n = -5.31662479 Simplifying n = -5.31662479Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.31662479, -5.31662479}Solution
n = {1.31662479, -5.31662479}
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