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Simplifying 5n2 + -12n + -8 = 0 Reorder the terms: -8 + -12n + 5n2 = 0 Solving -8 + -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'. -1.6 + -2.4n + n2 = 0 Move the constant term to the right: Add '1.6' to each side of the equation. -1.6 + -2.4n + 1.6 + n2 = 0 + 1.6 Reorder the terms: -1.6 + 1.6 + -2.4n + n2 = 0 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + -2.4n + n2 = 0 + 1.6 -2.4n + n2 = 0 + 1.6 Combine like terms: 0 + 1.6 = 1.6 -2.4n + n2 = 1.6 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 = 1.6 + 1.44 Reorder the terms: 1.44 + -2.4n + n2 = 1.6 + 1.44 Combine like terms: 1.6 + 1.44 = 3.04 1.44 + -2.4n + n2 = 3.04 Factor a perfect square on the left side: (n + -1.2)(n + -1.2) = 3.04 Calculate the square root of the right side: 1.743559577 Break this problem into two subproblems by setting (n + -1.2) equal to 1.743559577 and -1.743559577.Subproblem 1
n + -1.2 = 1.743559577 Simplifying n + -1.2 = 1.743559577 Reorder the terms: -1.2 + n = 1.743559577 Solving -1.2 + n = 1.743559577 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 = 1.743559577 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + n = 1.743559577 + 1.2 n = 1.743559577 + 1.2 Combine like terms: 1.743559577 + 1.2 = 2.943559577 n = 2.943559577 Simplifying n = 2.943559577Subproblem 2
n + -1.2 = -1.743559577 Simplifying n + -1.2 = -1.743559577 Reorder the terms: -1.2 + n = -1.743559577 Solving -1.2 + n = -1.743559577 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 = -1.743559577 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + n = -1.743559577 + 1.2 n = -1.743559577 + 1.2 Combine like terms: -1.743559577 + 1.2 = -0.543559577 n = -0.543559577 Simplifying n = -0.543559577Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.943559577, -0.543559577}
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