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Simplifying n * n = 90 + -1n Multiply n * n n2 = 90 + -1n Solving n2 = 90 + -1n Solving for variable 'n'. Reorder the terms: -90 + n + n2 = 90 + -1n + -90 + n Reorder the terms: -90 + n + n2 = 90 + -90 + -1n + n Combine like terms: 90 + -90 = 0 -90 + n + n2 = 0 + -1n + n -90 + n + n2 = -1n + n Combine like terms: -1n + n = 0 -90 + n + n2 = 0 Factor a trinomial. (-10 + -1n)(9 + -1n) = 0Subproblem 1
Set the factor '(-10 + -1n)' equal to zero and attempt to solve: Simplifying -10 + -1n = 0 Solving -10 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + -1n = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -1n = 0 + 10 -1n = 0 + 10 Combine like terms: 0 + 10 = 10 -1n = 10 Divide each side by '-1'. n = -10 Simplifying n = -10Subproblem 2
Set the factor '(9 + -1n)' equal to zero and attempt to solve: Simplifying 9 + -1n = 0 Solving 9 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1n = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1n = 0 + -9 -1n = 0 + -9 Combine like terms: 0 + -9 = -9 -1n = -9 Divide each side by '-1'. n = 9 Simplifying n = 9Solution
n = {-10, 9}
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