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Simplifying 5n2 + -3n + -96 = 0 Reorder the terms: -96 + -3n + 5n2 = 0 Solving -96 + -3n + 5n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -19.2 + -0.6n + n2 = 0 Move the constant term to the right: Add '19.2' to each side of the equation. -19.2 + -0.6n + 19.2 + n2 = 0 + 19.2 Reorder the terms: -19.2 + 19.2 + -0.6n + n2 = 0 + 19.2 Combine like terms: -19.2 + 19.2 = 0.0 0.0 + -0.6n + n2 = 0 + 19.2 -0.6n + n2 = 0 + 19.2 Combine like terms: 0 + 19.2 = 19.2 -0.6n + n2 = 19.2 The n term is -0.6n. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6n + 0.09 + n2 = 19.2 + 0.09 Reorder the terms: 0.09 + -0.6n + n2 = 19.2 + 0.09 Combine like terms: 19.2 + 0.09 = 19.29 0.09 + -0.6n + n2 = 19.29 Factor a perfect square on the left side: (n + -0.3)(n + -0.3) = 19.29 Calculate the square root of the right side: 4.392038251 Break this problem into two subproblems by setting (n + -0.3) equal to 4.392038251 and -4.392038251.Subproblem 1
n + -0.3 = 4.392038251 Simplifying n + -0.3 = 4.392038251 Reorder the terms: -0.3 + n = 4.392038251 Solving -0.3 + n = 4.392038251 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + n = 4.392038251 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + n = 4.392038251 + 0.3 n = 4.392038251 + 0.3 Combine like terms: 4.392038251 + 0.3 = 4.692038251 n = 4.692038251 Simplifying n = 4.692038251Subproblem 2
n + -0.3 = -4.392038251 Simplifying n + -0.3 = -4.392038251 Reorder the terms: -0.3 + n = -4.392038251 Solving -0.3 + n = -4.392038251 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + n = -4.392038251 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + n = -4.392038251 + 0.3 n = -4.392038251 + 0.3 Combine like terms: -4.392038251 + 0.3 = -4.092038251 n = -4.092038251 Simplifying n = -4.092038251Solution
The solution to the problem is based on the solutions from the subproblems. n = {4.692038251, -4.092038251}
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