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Simplifying 2n2 = -7 + 15n Solving 2n2 = -7 + 15n Solving for variable 'n'. Reorder the terms: 7 + -15n + 2n2 = -7 + 15n + 7 + -15n Reorder the terms: 7 + -15n + 2n2 = -7 + 7 + 15n + -15n Combine like terms: -7 + 7 = 0 7 + -15n + 2n2 = 0 + 15n + -15n 7 + -15n + 2n2 = 15n + -15n Combine like terms: 15n + -15n = 0 7 + -15n + 2n2 = 0 Factor a trinomial. (1 + -2n)(7 + -1n) = 0Subproblem 1
Set the factor '(1 + -2n)' equal to zero and attempt to solve: Simplifying 1 + -2n = 0 Solving 1 + -2n = 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 + -2n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2n = 0 + -1 -2n = 0 + -1 Combine like terms: 0 + -1 = -1 -2n = -1 Divide each side by '-2'. n = 0.5 Simplifying n = 0.5Subproblem 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 = {0.5, 7}
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