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Simplifying 29n2 + -76n = n2 + -40 Reorder the terms: -76n + 29n2 = n2 + -40 Reorder the terms: -76n + 29n2 = -40 + n2 Solving -76n + 29n2 = -40 + n2 Solving for variable 'n'. Reorder the terms: 40 + -76n + 29n2 + -1n2 = -40 + n2 + 40 + -1n2 Combine like terms: 29n2 + -1n2 = 28n2 40 + -76n + 28n2 = -40 + n2 + 40 + -1n2 Reorder the terms: 40 + -76n + 28n2 = -40 + 40 + n2 + -1n2 Combine like terms: -40 + 40 = 0 40 + -76n + 28n2 = 0 + n2 + -1n2 40 + -76n + 28n2 = n2 + -1n2 Combine like terms: n2 + -1n2 = 0 40 + -76n + 28n2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(10 + -19n + 7n2) = 0 Factor a trinomial. 4((5 + -7n)(2 + -1n)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(5 + -7n)' equal to zero and attempt to solve: Simplifying 5 + -7n = 0 Solving 5 + -7n = 0 Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -7n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -7n = 0 + -5 -7n = 0 + -5 Combine like terms: 0 + -5 = -5 -7n = -5 Divide each side by '-7'. n = 0.7142857143 Simplifying n = 0.7142857143Subproblem 2
Set the factor '(2 + -1n)' equal to zero and attempt to solve: Simplifying 2 + -1n = 0 Solving 2 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1n = 0 + -2 -1n = 0 + -2 Combine like terms: 0 + -2 = -2 -1n = -2 Divide each side by '-1'. n = 2 Simplifying n = 2Solution
n = {0.7142857143, 2}
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