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Simplifying 5n2 + 7n + -51 = 0 Reorder the terms: -51 + 7n + 5n2 = 0 Solving -51 + 7n + 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'. -10.2 + 1.4n + n2 = 0 Move the constant term to the right: Add '10.2' to each side of the equation. -10.2 + 1.4n + 10.2 + n2 = 0 + 10.2 Reorder the terms: -10.2 + 10.2 + 1.4n + n2 = 0 + 10.2 Combine like terms: -10.2 + 10.2 = 0.0 0.0 + 1.4n + n2 = 0 + 10.2 1.4n + n2 = 0 + 10.2 Combine like terms: 0 + 10.2 = 10.2 1.4n + n2 = 10.2 The n term is 1.4n. Take half its coefficient (0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. 1.4n + 0.49 + n2 = 10.2 + 0.49 Reorder the terms: 0.49 + 1.4n + n2 = 10.2 + 0.49 Combine like terms: 10.2 + 0.49 = 10.69 0.49 + 1.4n + n2 = 10.69 Factor a perfect square on the left side: (n + 0.7)(n + 0.7) = 10.69 Calculate the square root of the right side: 3.269556545 Break this problem into two subproblems by setting (n + 0.7) equal to 3.269556545 and -3.269556545.Subproblem 1
n + 0.7 = 3.269556545 Simplifying n + 0.7 = 3.269556545 Reorder the terms: 0.7 + n = 3.269556545 Solving 0.7 + n = 3.269556545 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + n = 3.269556545 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + n = 3.269556545 + -0.7 n = 3.269556545 + -0.7 Combine like terms: 3.269556545 + -0.7 = 2.569556545 n = 2.569556545 Simplifying n = 2.569556545Subproblem 2
n + 0.7 = -3.269556545 Simplifying n + 0.7 = -3.269556545 Reorder the terms: 0.7 + n = -3.269556545 Solving 0.7 + n = -3.269556545 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + n = -3.269556545 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + n = -3.269556545 + -0.7 n = -3.269556545 + -0.7 Combine like terms: -3.269556545 + -0.7 = -3.969556545 n = -3.969556545 Simplifying n = -3.969556545Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.569556545, -3.969556545}
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