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Simplifying 55 = 7(n + 4) * 2n Reorder the terms: 55 = 7(4 + n) * 2n Reorder the terms for easier multiplication: 55 = 7 * 2n(4 + n) Multiply 7 * 2 55 = 14n(4 + n) 55 = (4 * 14n + n * 14n) 55 = (56n + 14n2) Solving 55 = 56n + 14n2 Solving for variable 'n'. Reorder the terms: 55 + -56n + -14n2 = 56n + -56n + 14n2 + -14n2 Combine like terms: 56n + -56n = 0 55 + -56n + -14n2 = 0 + 14n2 + -14n2 55 + -56n + -14n2 = 14n2 + -14n2 Combine like terms: 14n2 + -14n2 = 0 55 + -56n + -14n2 = 0 Begin completing the square. Divide all terms by -14 the coefficient of the squared term: Divide each side by '-14'. -3.928571429 + 4n + n2 = 0 Move the constant term to the right: Add '3.928571429' to each side of the equation. -3.928571429 + 4n + 3.928571429 + n2 = 0 + 3.928571429 Reorder the terms: -3.928571429 + 3.928571429 + 4n + n2 = 0 + 3.928571429 Combine like terms: -3.928571429 + 3.928571429 = 0.000000000 0.000000000 + 4n + n2 = 0 + 3.928571429 4n + n2 = 0 + 3.928571429 Combine like terms: 0 + 3.928571429 = 3.928571429 4n + n2 = 3.928571429 The n term is 4n. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4n + 4 + n2 = 3.928571429 + 4 Reorder the terms: 4 + 4n + n2 = 3.928571429 + 4 Combine like terms: 3.928571429 + 4 = 7.928571429 4 + 4n + n2 = 7.928571429 Factor a perfect square on the left side: (n + 2)(n + 2) = 7.928571429 Calculate the square root of the right side: 2.815771906 Break this problem into two subproblems by setting (n + 2) equal to 2.815771906 and -2.815771906.Subproblem 1
n + 2 = 2.815771906 Simplifying n + 2 = 2.815771906 Reorder the terms: 2 + n = 2.815771906 Solving 2 + n = 2.815771906 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + n = 2.815771906 + -2 Combine like terms: 2 + -2 = 0 0 + n = 2.815771906 + -2 n = 2.815771906 + -2 Combine like terms: 2.815771906 + -2 = 0.815771906 n = 0.815771906 Simplifying n = 0.815771906Subproblem 2
n + 2 = -2.815771906 Simplifying n + 2 = -2.815771906 Reorder the terms: 2 + n = -2.815771906 Solving 2 + n = -2.815771906 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + n = -2.815771906 + -2 Combine like terms: 2 + -2 = 0 0 + n = -2.815771906 + -2 n = -2.815771906 + -2 Combine like terms: -2.815771906 + -2 = -4.815771906 n = -4.815771906 Simplifying n = -4.815771906Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.815771906, -4.815771906}
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