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Simplifying 5n2 + -6n + -10 = 0 Reorder the terms: -10 + -6n + 5n2 = 0 Solving -10 + -6n + 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'. -2 + -1.2n + n2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -1.2n + 2 + n2 = 0 + 2 Reorder the terms: -2 + 2 + -1.2n + n2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1.2n + n2 = 0 + 2 -1.2n + n2 = 0 + 2 Combine like terms: 0 + 2 = 2 -1.2n + n2 = 2 The n term is -1.2n. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2n + 0.36 + n2 = 2 + 0.36 Reorder the terms: 0.36 + -1.2n + n2 = 2 + 0.36 Combine like terms: 2 + 0.36 = 2.36 0.36 + -1.2n + n2 = 2.36 Factor a perfect square on the left side: (n + -0.6)(n + -0.6) = 2.36 Calculate the square root of the right side: 1.53622915 Break this problem into two subproblems by setting (n + -0.6) equal to 1.53622915 and -1.53622915.Subproblem 1
n + -0.6 = 1.53622915 Simplifying n + -0.6 = 1.53622915 Reorder the terms: -0.6 + n = 1.53622915 Solving -0.6 + n = 1.53622915 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + n = 1.53622915 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + n = 1.53622915 + 0.6 n = 1.53622915 + 0.6 Combine like terms: 1.53622915 + 0.6 = 2.13622915 n = 2.13622915 Simplifying n = 2.13622915Subproblem 2
n + -0.6 = -1.53622915 Simplifying n + -0.6 = -1.53622915 Reorder the terms: -0.6 + n = -1.53622915 Solving -0.6 + n = -1.53622915 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + n = -1.53622915 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + n = -1.53622915 + 0.6 n = -1.53622915 + 0.6 Combine like terms: -1.53622915 + 0.6 = -0.93622915 n = -0.93622915 Simplifying n = -0.93622915Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.13622915, -0.93622915}
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