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Simplifying 4n2 + 16n + -60 = 0 Reorder the terms: -60 + 16n + 4n2 = 0 Solving -60 + 16n + 4n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '4'. 4(-15 + 4n + n2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-15 + 4n + n2)' equal to zero and attempt to solve: Simplifying -15 + 4n + n2 = 0 Solving -15 + 4n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + 4n + 15 + n2 = 0 + 15 Reorder the terms: -15 + 15 + 4n + n2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 4n + n2 = 0 + 15 4n + n2 = 0 + 15 Combine like terms: 0 + 15 = 15 4n + n2 = 15 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 = 15 + 4 Reorder the terms: 4 + 4n + n2 = 15 + 4 Combine like terms: 15 + 4 = 19 4 + 4n + n2 = 19 Factor a perfect square on the left side: (n + 2)(n + 2) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (n + 2) equal to 4.358898944 and -4.358898944.Subproblem 1
n + 2 = 4.358898944 Simplifying n + 2 = 4.358898944 Reorder the terms: 2 + n = 4.358898944 Solving 2 + n = 4.358898944 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 = 4.358898944 + -2 Combine like terms: 2 + -2 = 0 0 + n = 4.358898944 + -2 n = 4.358898944 + -2 Combine like terms: 4.358898944 + -2 = 2.358898944 n = 2.358898944 Simplifying n = 2.358898944Subproblem 2
n + 2 = -4.358898944 Simplifying n + 2 = -4.358898944 Reorder the terms: 2 + n = -4.358898944 Solving 2 + n = -4.358898944 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 = -4.358898944 + -2 Combine like terms: 2 + -2 = 0 0 + n = -4.358898944 + -2 n = -4.358898944 + -2 Combine like terms: -4.358898944 + -2 = -6.358898944 n = -6.358898944 Simplifying n = -6.358898944Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.358898944, -6.358898944}Solution
n = {2.358898944, -6.358898944}
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