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Simplifying 4n2 = -40n + -100 Reorder the terms: 4n2 = -100 + -40n Solving 4n2 = -100 + -40n Solving for variable 'n'. Reorder the terms: 100 + 40n + 4n2 = -100 + -40n + 100 + 40n Reorder the terms: 100 + 40n + 4n2 = -100 + 100 + -40n + 40n Combine like terms: -100 + 100 = 0 100 + 40n + 4n2 = 0 + -40n + 40n 100 + 40n + 4n2 = -40n + 40n Combine like terms: -40n + 40n = 0 100 + 40n + 4n2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(25 + 10n + n2) = 0 Factor a trinomial. 4((5 + n)(5 + n)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(5 + n)' equal to zero and attempt to solve: Simplifying 5 + n = 0 Solving 5 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + n = 0 + -5 n = 0 + -5 Combine like terms: 0 + -5 = -5 n = -5 Simplifying n = -5Subproblem 2
Set the factor '(5 + n)' equal to zero and attempt to solve: Simplifying 5 + n = 0 Solving 5 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + n = 0 + -5 n = 0 + -5 Combine like terms: 0 + -5 = -5 n = -5 Simplifying n = -5Solution
n = {-5, -5}
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