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Simplifying 5n2 + 12n + -5 = 0 Reorder the terms: -5 + 12n + 5n2 = 0 Solving -5 + 12n + 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'. -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 = 2.44 1.44 + 2.4n + n2 = 2.44 Factor a perfect square on the left side: (n + 1.2)(n + 1.2) = 2.44 Calculate the square root of the right side: 1.562049935 Break this problem into two subproblems by setting (n + 1.2) equal to 1.562049935 and -1.562049935.Subproblem 1
n + 1.2 = 1.562049935 Simplifying n + 1.2 = 1.562049935 Reorder the terms: 1.2 + n = 1.562049935 Solving 1.2 + n = 1.562049935 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 = 1.562049935 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + n = 1.562049935 + -1.2 n = 1.562049935 + -1.2 Combine like terms: 1.562049935 + -1.2 = 0.362049935 n = 0.362049935 Simplifying n = 0.362049935Subproblem 2
n + 1.2 = -1.562049935 Simplifying n + 1.2 = -1.562049935 Reorder the terms: 1.2 + n = -1.562049935 Solving 1.2 + n = -1.562049935 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 = -1.562049935 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + n = -1.562049935 + -1.2 n = -1.562049935 + -1.2 Combine like terms: -1.562049935 + -1.2 = -2.762049935 n = -2.762049935 Simplifying n = -2.762049935Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.362049935, -2.762049935}
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