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Simplifying (5n + 29)(n + -8) = 8 Reorder the terms: (29 + 5n)(n + -8) = 8 Reorder the terms: (29 + 5n)(-8 + n) = 8 Multiply (29 + 5n) * (-8 + n) (29(-8 + n) + 5n * (-8 + n)) = 8 ((-8 * 29 + n * 29) + 5n * (-8 + n)) = 8 ((-232 + 29n) + 5n * (-8 + n)) = 8 (-232 + 29n + (-8 * 5n + n * 5n)) = 8 (-232 + 29n + (-40n + 5n2)) = 8 Combine like terms: 29n + -40n = -11n (-232 + -11n + 5n2) = 8 Solving -232 + -11n + 5n2 = 8 Solving for variable 'n'. Reorder the terms: -232 + -8 + -11n + 5n2 = 8 + -8 Combine like terms: -232 + -8 = -240 -240 + -11n + 5n2 = 8 + -8 Combine like terms: 8 + -8 = 0 -240 + -11n + 5n2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -48 + -2.2n + n2 = 0 Move the constant term to the right: Add '48' to each side of the equation. -48 + -2.2n + 48 + n2 = 0 + 48 Reorder the terms: -48 + 48 + -2.2n + n2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + -2.2n + n2 = 0 + 48 -2.2n + n2 = 0 + 48 Combine like terms: 0 + 48 = 48 -2.2n + n2 = 48 The n term is -2.2n. Take half its coefficient (-1.1). Square it (1.21) and add it to both sides. Add '1.21' to each side of the equation. -2.2n + 1.21 + n2 = 48 + 1.21 Reorder the terms: 1.21 + -2.2n + n2 = 48 + 1.21 Combine like terms: 48 + 1.21 = 49.21 1.21 + -2.2n + n2 = 49.21 Factor a perfect square on the left side: (n + -1.1)(n + -1.1) = 49.21 Calculate the square root of the right side: 7.014983963 Break this problem into two subproblems by setting (n + -1.1) equal to 7.014983963 and -7.014983963.Subproblem 1
n + -1.1 = 7.014983963 Simplifying n + -1.1 = 7.014983963 Reorder the terms: -1.1 + n = 7.014983963 Solving -1.1 + n = 7.014983963 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + n = 7.014983963 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + n = 7.014983963 + 1.1 n = 7.014983963 + 1.1 Combine like terms: 7.014983963 + 1.1 = 8.114983963 n = 8.114983963 Simplifying n = 8.114983963Subproblem 2
n + -1.1 = -7.014983963 Simplifying n + -1.1 = -7.014983963 Reorder the terms: -1.1 + n = -7.014983963 Solving -1.1 + n = -7.014983963 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + n = -7.014983963 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + n = -7.014983963 + 1.1 n = -7.014983963 + 1.1 Combine like terms: -7.014983963 + 1.1 = -5.914983963 n = -5.914983963 Simplifying n = -5.914983963Solution
The solution to the problem is based on the solutions from the subproblems. n = {8.114983963, -5.914983963}
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