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Simplifying 5n2 + -6 = 30n Reorder the terms: -6 + 5n2 = 30n Solving -6 + 5n2 = 30n Solving for variable 'n'. Reorder the terms: -6 + -30n + 5n2 = 30n + -30n Combine like terms: 30n + -30n = 0 -6 + -30n + 5n2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.2 + -6n + n2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + -6n + 1.2 + n2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + -6n + n2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + -6n + n2 = 0 + 1.2 -6n + n2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 -6n + n2 = 1.2 The n term is -6n. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6n + 9 + n2 = 1.2 + 9 Reorder the terms: 9 + -6n + n2 = 1.2 + 9 Combine like terms: 1.2 + 9 = 10.2 9 + -6n + n2 = 10.2 Factor a perfect square on the left side: (n + -3)(n + -3) = 10.2 Calculate the square root of the right side: 3.193743885 Break this problem into two subproblems by setting (n + -3) equal to 3.193743885 and -3.193743885.Subproblem 1
n + -3 = 3.193743885 Simplifying n + -3 = 3.193743885 Reorder the terms: -3 + n = 3.193743885 Solving -3 + n = 3.193743885 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + n = 3.193743885 + 3 Combine like terms: -3 + 3 = 0 0 + n = 3.193743885 + 3 n = 3.193743885 + 3 Combine like terms: 3.193743885 + 3 = 6.193743885 n = 6.193743885 Simplifying n = 6.193743885Subproblem 2
n + -3 = -3.193743885 Simplifying n + -3 = -3.193743885 Reorder the terms: -3 + n = -3.193743885 Solving -3 + n = -3.193743885 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + n = -3.193743885 + 3 Combine like terms: -3 + 3 = 0 0 + n = -3.193743885 + 3 n = -3.193743885 + 3 Combine like terms: -3.193743885 + 3 = -0.193743885 n = -0.193743885 Simplifying n = -0.193743885Solution
The solution to the problem is based on the solutions from the subproblems. n = {6.193743885, -0.193743885}
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