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Simplifying 5n2 = -12n + -2 Reorder the terms: 5n2 = -2 + -12n Solving 5n2 = -2 + -12n Solving for variable 'n'. Reorder the terms: 2 + 12n + 5n2 = -2 + -12n + 2 + 12n Reorder the terms: 2 + 12n + 5n2 = -2 + 2 + -12n + 12n Combine like terms: -2 + 2 = 0 2 + 12n + 5n2 = 0 + -12n + 12n 2 + 12n + 5n2 = -12n + 12n Combine like terms: -12n + 12n = 0 2 + 12n + 5n2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.4 + 2.4n + n2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + 2.4n + -0.4 + n2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + 2.4n + n2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + 2.4n + n2 = 0 + -0.4 2.4n + n2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 2.4n + n2 = -0.4 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 = -0.4 + 1.44 Reorder the terms: 1.44 + 2.4n + n2 = -0.4 + 1.44 Combine like terms: -0.4 + 1.44 = 1.04 1.44 + 2.4n + n2 = 1.04 Factor a perfect square on the left side: (n + 1.2)(n + 1.2) = 1.04 Calculate the square root of the right side: 1.019803903 Break this problem into two subproblems by setting (n + 1.2) equal to 1.019803903 and -1.019803903.Subproblem 1
n + 1.2 = 1.019803903 Simplifying n + 1.2 = 1.019803903 Reorder the terms: 1.2 + n = 1.019803903 Solving 1.2 + n = 1.019803903 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 = 1.019803903 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + n = 1.019803903 + -1.2 n = 1.019803903 + -1.2 Combine like terms: 1.019803903 + -1.2 = -0.180196097 n = -0.180196097 Simplifying n = -0.180196097Subproblem 2
n + 1.2 = -1.019803903 Simplifying n + 1.2 = -1.019803903 Reorder the terms: 1.2 + n = -1.019803903 Solving 1.2 + n = -1.019803903 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 = -1.019803903 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + n = -1.019803903 + -1.2 n = -1.019803903 + -1.2 Combine like terms: -1.019803903 + -1.2 = -2.219803903 n = -2.219803903 Simplifying n = -2.219803903Solution
The solution to the problem is based on the solutions from the subproblems. n = {-0.180196097, -2.219803903}
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