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Simplifying n2 + 23n + 13 = 0 Reorder the terms: 13 + 23n + n2 = 0 Solving 13 + 23n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '-13' to each side of the equation. 13 + 23n + -13 + n2 = 0 + -13 Reorder the terms: 13 + -13 + 23n + n2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 23n + n2 = 0 + -13 23n + n2 = 0 + -13 Combine like terms: 0 + -13 = -13 23n + n2 = -13 The n term is 23n. Take half its coefficient (11.5). Square it (132.25) and add it to both sides. Add '132.25' to each side of the equation. 23n + 132.25 + n2 = -13 + 132.25 Reorder the terms: 132.25 + 23n + n2 = -13 + 132.25 Combine like terms: -13 + 132.25 = 119.25 132.25 + 23n + n2 = 119.25 Factor a perfect square on the left side: (n + 11.5)(n + 11.5) = 119.25 Calculate the square root of the right side: 10.920164834 Break this problem into two subproblems by setting (n + 11.5) equal to 10.920164834 and -10.920164834.Subproblem 1
n + 11.5 = 10.920164834 Simplifying n + 11.5 = 10.920164834 Reorder the terms: 11.5 + n = 10.920164834 Solving 11.5 + n = 10.920164834 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-11.5' to each side of the equation. 11.5 + -11.5 + n = 10.920164834 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + n = 10.920164834 + -11.5 n = 10.920164834 + -11.5 Combine like terms: 10.920164834 + -11.5 = -0.579835166 n = -0.579835166 Simplifying n = -0.579835166Subproblem 2
n + 11.5 = -10.920164834 Simplifying n + 11.5 = -10.920164834 Reorder the terms: 11.5 + n = -10.920164834 Solving 11.5 + n = -10.920164834 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-11.5' to each side of the equation. 11.5 + -11.5 + n = -10.920164834 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + n = -10.920164834 + -11.5 n = -10.920164834 + -11.5 Combine like terms: -10.920164834 + -11.5 = -22.420164834 n = -22.420164834 Simplifying n = -22.420164834Solution
The solution to the problem is based on the solutions from the subproblems. n = {-0.579835166, -22.420164834}
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