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Simplifying 4n2 = 9n + 100 Reorder the terms: 4n2 = 100 + 9n Solving 4n2 = 100 + 9n Solving for variable 'n'. Reorder the terms: -100 + -9n + 4n2 = 100 + 9n + -100 + -9n Reorder the terms: -100 + -9n + 4n2 = 100 + -100 + 9n + -9n Combine like terms: 100 + -100 = 0 -100 + -9n + 4n2 = 0 + 9n + -9n -100 + -9n + 4n2 = 9n + -9n Combine like terms: 9n + -9n = 0 -100 + -9n + 4n2 = 0 Factor a trinomial. (-4 + -1n)(25 + -4n) = 0Subproblem 1
Set the factor '(-4 + -1n)' equal to zero and attempt to solve: Simplifying -4 + -1n = 0 Solving -4 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1n = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1n = 0 + 4 -1n = 0 + 4 Combine like terms: 0 + 4 = 4 -1n = 4 Divide each side by '-1'. n = -4 Simplifying n = -4Subproblem 2
Set the factor '(25 + -4n)' equal to zero and attempt to solve: Simplifying 25 + -4n = 0 Solving 25 + -4n = 0 Move all terms containing n to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + -4n = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -4n = 0 + -25 -4n = 0 + -25 Combine like terms: 0 + -25 = -25 -4n = -25 Divide each side by '-4'. n = 6.25 Simplifying n = 6.25Solution
n = {-4, 6.25}
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