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Simplifying 2n(n + -3) = 5(n + 3) Reorder the terms: 2n(-3 + n) = 5(n + 3) (-3 * 2n + n * 2n) = 5(n + 3) (-6n + 2n2) = 5(n + 3) Reorder the terms: -6n + 2n2 = 5(3 + n) -6n + 2n2 = (3 * 5 + n * 5) -6n + 2n2 = (15 + 5n) Solving -6n + 2n2 = 15 + 5n Solving for variable 'n'. Reorder the terms: -15 + -6n + -5n + 2n2 = 15 + 5n + -15 + -5n Combine like terms: -6n + -5n = -11n -15 + -11n + 2n2 = 15 + 5n + -15 + -5n Reorder the terms: -15 + -11n + 2n2 = 15 + -15 + 5n + -5n Combine like terms: 15 + -15 = 0 -15 + -11n + 2n2 = 0 + 5n + -5n -15 + -11n + 2n2 = 5n + -5n Combine like terms: 5n + -5n = 0 -15 + -11n + 2n2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -7.5 + -5.5n + n2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + -5.5n + 7.5 + n2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + -5.5n + n2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + -5.5n + n2 = 0 + 7.5 -5.5n + n2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 -5.5n + n2 = 7.5 The n term is -5.5n. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5n + 7.5625 + n2 = 7.5 + 7.5625 Reorder the terms: 7.5625 + -5.5n + n2 = 7.5 + 7.5625 Combine like terms: 7.5 + 7.5625 = 15.0625 7.5625 + -5.5n + n2 = 15.0625 Factor a perfect square on the left side: (n + -2.75)(n + -2.75) = 15.0625 Calculate the square root of the right side: 3.881043674 Break this problem into two subproblems by setting (n + -2.75) equal to 3.881043674 and -3.881043674.Subproblem 1
n + -2.75 = 3.881043674 Simplifying n + -2.75 = 3.881043674 Reorder the terms: -2.75 + n = 3.881043674 Solving -2.75 + n = 3.881043674 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + n = 3.881043674 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + n = 3.881043674 + 2.75 n = 3.881043674 + 2.75 Combine like terms: 3.881043674 + 2.75 = 6.631043674 n = 6.631043674 Simplifying n = 6.631043674Subproblem 2
n + -2.75 = -3.881043674 Simplifying n + -2.75 = -3.881043674 Reorder the terms: -2.75 + n = -3.881043674 Solving -2.75 + n = -3.881043674 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + n = -3.881043674 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + n = -3.881043674 + 2.75 n = -3.881043674 + 2.75 Combine like terms: -3.881043674 + 2.75 = -1.131043674 n = -1.131043674 Simplifying n = -1.131043674Solution
The solution to the problem is based on the solutions from the subproblems. n = {6.631043674, -1.131043674}
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