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Simplifying 5n2 = -12n + -5 Reorder the terms: 5n2 = -5 + -12n Solving 5n2 = -5 + -12n Solving for variable 'n'. Reorder the terms: 5 + 12n + 5n2 = -5 + -12n + 5 + 12n Reorder the terms: 5 + 12n + 5n2 = -5 + 5 + -12n + 12n Combine like terms: -5 + 5 = 0 5 + 12n + 5n2 = 0 + -12n + 12n 5 + 12n + 5n2 = -12n + 12n Combine like terms: -12n + 12n = 0 5 + 12n + 5n2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1 + 2.4n + n2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 2.4n + -1 + n2 = 0 + -1 Reorder the terms: 1 + -1 + 2.4n + n2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2.4n + n2 = 0 + -1 2.4n + n2 = 0 + -1 Combine like terms: 0 + -1 = -1 2.4n + n2 = -1 The n term is 2.4n. Take half its coefficient (1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. 2.4n + 1.44 + n2 = -1 + 1.44 Reorder the terms: 1.44 + 2.4n + n2 = -1 + 1.44 Combine like terms: -1 + 1.44 = 0.44 1.44 + 2.4n + n2 = 0.44 Factor a perfect square on the left side: (n + 1.2)(n + 1.2) = 0.44 Calculate the square root of the right side: 0.663324958 Break this problem into two subproblems by setting (n + 1.2) equal to 0.663324958 and -0.663324958.Subproblem 1
n + 1.2 = 0.663324958 Simplifying n + 1.2 = 0.663324958 Reorder the terms: 1.2 + n = 0.663324958 Solving 1.2 + n = 0.663324958 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + n = 0.663324958 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + n = 0.663324958 + -1.2 n = 0.663324958 + -1.2 Combine like terms: 0.663324958 + -1.2 = -0.536675042 n = -0.536675042 Simplifying n = -0.536675042Subproblem 2
n + 1.2 = -0.663324958 Simplifying n + 1.2 = -0.663324958 Reorder the terms: 1.2 + n = -0.663324958 Solving 1.2 + n = -0.663324958 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + n = -0.663324958 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + n = -0.663324958 + -1.2 n = -0.663324958 + -1.2 Combine like terms: -0.663324958 + -1.2 = -1.863324958 n = -1.863324958 Simplifying n = -1.863324958Solution
The solution to the problem is based on the solutions from the subproblems. n = {-0.536675042, -1.863324958}
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