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Simplifying 72 + n2 = 30n Solving 72 + n2 = 30n Solving for variable 'n'. Reorder the terms: 72 + -30n + n2 = 30n + -30n Combine like terms: 30n + -30n = 0 72 + -30n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-72' to each side of the equation. 72 + -30n + -72 + n2 = 0 + -72 Reorder the terms: 72 + -72 + -30n + n2 = 0 + -72 Combine like terms: 72 + -72 = 0 0 + -30n + n2 = 0 + -72 -30n + n2 = 0 + -72 Combine like terms: 0 + -72 = -72 -30n + n2 = -72 The n term is -30n. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30n + 225 + n2 = -72 + 225 Reorder the terms: 225 + -30n + n2 = -72 + 225 Combine like terms: -72 + 225 = 153 225 + -30n + n2 = 153 Factor a perfect square on the left side: (n + -15)(n + -15) = 153 Calculate the square root of the right side: 12.369316877 Break this problem into two subproblems by setting (n + -15) equal to 12.369316877 and -12.369316877.Subproblem 1
n + -15 = 12.369316877 Simplifying n + -15 = 12.369316877 Reorder the terms: -15 + n = 12.369316877 Solving -15 + n = 12.369316877 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + n = 12.369316877 + 15 Combine like terms: -15 + 15 = 0 0 + n = 12.369316877 + 15 n = 12.369316877 + 15 Combine like terms: 12.369316877 + 15 = 27.369316877 n = 27.369316877 Simplifying n = 27.369316877Subproblem 2
n + -15 = -12.369316877 Simplifying n + -15 = -12.369316877 Reorder the terms: -15 + n = -12.369316877 Solving -15 + n = -12.369316877 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + n = -12.369316877 + 15 Combine like terms: -15 + 15 = 0 0 + n = -12.369316877 + 15 n = -12.369316877 + 15 Combine like terms: -12.369316877 + 15 = 2.630683123 n = 2.630683123 Simplifying n = 2.630683123Solution
The solution to the problem is based on the solutions from the subproblems. n = {27.369316877, 2.630683123}
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