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Simplifying 81n2 + -99np + 28p2 = 0 Reorder the terms: -99np + 81n2 + 28p2 = 0 Solving -99np + 81n2 + 28p2 = 0 Solving for variable 'n'. Factor a trinomial. (9n + -7p)(9n + -4p) = 0Subproblem 1
Set the factor '(9n + -7p)' equal to zero and attempt to solve: Simplifying 9n + -7p = 0 Solving 9n + -7p = 0 Move all terms containing n to the left, all other terms to the right. Add '7p' to each side of the equation. 9n + -7p + 7p = 0 + 7p Combine like terms: -7p + 7p = 0 9n + 0 = 0 + 7p 9n = 0 + 7p Remove the zero: 9n = 7p Divide each side by '9'. n = 0.7777777778p Simplifying n = 0.7777777778pSubproblem 2
Set the factor '(9n + -4p)' equal to zero and attempt to solve: Simplifying 9n + -4p = 0 Solving 9n + -4p = 0 Move all terms containing n to the left, all other terms to the right. Add '4p' to each side of the equation. 9n + -4p + 4p = 0 + 4p Combine like terms: -4p + 4p = 0 9n + 0 = 0 + 4p 9n = 0 + 4p Remove the zero: 9n = 4p Divide each side by '9'. n = 0.4444444444p Simplifying n = 0.4444444444pSolution
n = {0.7777777778p, 0.4444444444p}
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