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Simplifying 7n2 = -42n + 49 Reorder the terms: 7n2 = 49 + -42n Solving 7n2 = 49 + -42n Solving for variable 'n'. Reorder the terms: -49 + 42n + 7n2 = 49 + -42n + -49 + 42n Reorder the terms: -49 + 42n + 7n2 = 49 + -49 + -42n + 42n Combine like terms: 49 + -49 = 0 -49 + 42n + 7n2 = 0 + -42n + 42n -49 + 42n + 7n2 = -42n + 42n Combine like terms: -42n + 42n = 0 -49 + 42n + 7n2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(-7 + 6n + n2) = 0 Factor a trinomial. 7((-7 + -1n)(1 + -1n)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(-7 + -1n)' equal to zero and attempt to solve: Simplifying -7 + -1n = 0 Solving -7 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -1n = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1n = 0 + 7 -1n = 0 + 7 Combine like terms: 0 + 7 = 7 -1n = 7 Divide each side by '-1'. n = -7 Simplifying n = -7Subproblem 2
Set the factor '(1 + -1n)' equal to zero and attempt to solve: Simplifying 1 + -1n = 0 Solving 1 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1n = 0 + -1 -1n = 0 + -1 Combine like terms: 0 + -1 = -1 -1n = -1 Divide each side by '-1'. n = 1 Simplifying n = 1Solution
n = {-7, 1}
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