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Simplifying 15 = 4.3n(n + -4) Reorder the terms: 15 = 4.3n(-4 + n) 15 = (-4 * 4.3n + n * 4.3n) 15 = (-17.2n + 4.3n2) Solving 15 = -17.2n + 4.3n2 Solving for variable 'n'. Reorder the terms: 15 + 17.2n + -4.3n2 = -17.2n + 17.2n + 4.3n2 + -4.3n2 Combine like terms: -17.2n + 17.2n = 0.0 15 + 17.2n + -4.3n2 = 0.0 + 4.3n2 + -4.3n2 15 + 17.2n + -4.3n2 = 4.3n2 + -4.3n2 Combine like terms: 4.3n2 + -4.3n2 = 0.0 15 + 17.2n + -4.3n2 = 0.0 Begin completing the square. Divide all terms by -4.3 the coefficient of the squared term: Divide each side by '-4.3'. -3.488372093 + -4n + n2 = 0 Move the constant term to the right: Add '3.488372093' to each side of the equation. -3.488372093 + -4n + 3.488372093 + n2 = 0 + 3.488372093 Reorder the terms: -3.488372093 + 3.488372093 + -4n + n2 = 0 + 3.488372093 Combine like terms: -3.488372093 + 3.488372093 = 0.000000000 0.000000000 + -4n + n2 = 0 + 3.488372093 -4n + n2 = 0 + 3.488372093 Combine like terms: 0 + 3.488372093 = 3.488372093 -4n + n2 = 3.488372093 The n term is -4n. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4n + 4 + n2 = 3.488372093 + 4 Reorder the terms: 4 + -4n + n2 = 3.488372093 + 4 Combine like terms: 3.488372093 + 4 = 7.488372093 4 + -4n + n2 = 7.488372093 Factor a perfect square on the left side: (n + -2)(n + -2) = 7.488372093 Calculate the square root of the right side: 2.736489008 Break this problem into two subproblems by setting (n + -2) equal to 2.736489008 and -2.736489008.Subproblem 1
n + -2 = 2.736489008 Simplifying n + -2 = 2.736489008 Reorder the terms: -2 + n = 2.736489008 Solving -2 + n = 2.736489008 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + n = 2.736489008 + 2 Combine like terms: -2 + 2 = 0 0 + n = 2.736489008 + 2 n = 2.736489008 + 2 Combine like terms: 2.736489008 + 2 = 4.736489008 n = 4.736489008 Simplifying n = 4.736489008Subproblem 2
n + -2 = -2.736489008 Simplifying n + -2 = -2.736489008 Reorder the terms: -2 + n = -2.736489008 Solving -2 + n = -2.736489008 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + n = -2.736489008 + 2 Combine like terms: -2 + 2 = 0 0 + n = -2.736489008 + 2 n = -2.736489008 + 2 Combine like terms: -2.736489008 + 2 = -0.736489008 n = -0.736489008 Simplifying n = -0.736489008Solution
The solution to the problem is based on the solutions from the subproblems. n = {4.736489008, -0.736489008}
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