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Simplifying 5n * n + -3n = 224 Multiply n * n 5n2 + -3n = 224 Reorder the terms: -3n + 5n2 = 224 Solving -3n + 5n2 = 224 Solving for variable 'n'. Reorder the terms: -224 + -3n + 5n2 = 224 + -224 Combine like terms: 224 + -224 = 0 -224 + -3n + 5n2 = 0 Factor a trinomial. (-32 + -5n)(7 + -1n) = 0Subproblem 1
Set the factor '(-32 + -5n)' equal to zero and attempt to solve: Simplifying -32 + -5n = 0 Solving -32 + -5n = 0 Move all terms containing n to the left, all other terms to the right. Add '32' to each side of the equation. -32 + 32 + -5n = 0 + 32 Combine like terms: -32 + 32 = 0 0 + -5n = 0 + 32 -5n = 0 + 32 Combine like terms: 0 + 32 = 32 -5n = 32 Divide each side by '-5'. n = -6.4 Simplifying n = -6.4Subproblem 2
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 = 7Solution
n = {-6.4, 7}
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