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Simplifying (7n2 + 4n) + -1(-6n2 + -5n + 2) = 0 Reorder the terms: (4n + 7n2) + -1(-6n2 + -5n + 2) = 0 Remove parenthesis around (4n + 7n2) 4n + 7n2 + -1(-6n2 + -5n + 2) = 0 Reorder the terms: 4n + 7n2 + -1(2 + -5n + -6n2) = 0 4n + 7n2 + (2 * -1 + -5n * -1 + -6n2 * -1) = 0 4n + 7n2 + (-2 + 5n + 6n2) = 0 Reorder the terms: -2 + 4n + 5n + 7n2 + 6n2 = 0 Combine like terms: 4n + 5n = 9n -2 + 9n + 7n2 + 6n2 = 0 Combine like terms: 7n2 + 6n2 = 13n2 -2 + 9n + 13n2 = 0 Solving -2 + 9n + 13n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -0.1538461538 + 0.6923076923n + n2 = 0 Move the constant term to the right: Add '0.1538461538' to each side of the equation. -0.1538461538 + 0.6923076923n + 0.1538461538 + n2 = 0 + 0.1538461538 Reorder the terms: -0.1538461538 + 0.1538461538 + 0.6923076923n + n2 = 0 + 0.1538461538 Combine like terms: -0.1538461538 + 0.1538461538 = 0.0000000000 0.0000000000 + 0.6923076923n + n2 = 0 + 0.1538461538 0.6923076923n + n2 = 0 + 0.1538461538 Combine like terms: 0 + 0.1538461538 = 0.1538461538 0.6923076923n + n2 = 0.1538461538 The n term is 0.6923076923n. Take half its coefficient (0.3461538462). Square it (0.1198224852) and add it to both sides. Add '0.1198224852' to each side of the equation. 0.6923076923n + 0.1198224852 + n2 = 0.1538461538 + 0.1198224852 Reorder the terms: 0.1198224852 + 0.6923076923n + n2 = 0.1538461538 + 0.1198224852 Combine like terms: 0.1538461538 + 0.1198224852 = 0.273668639 0.1198224852 + 0.6923076923n + n2 = 0.273668639 Factor a perfect square on the left side: (n + 0.3461538462)(n + 0.3461538462) = 0.273668639 Calculate the square root of the right side: 0.523133481 Break this problem into two subproblems by setting (n + 0.3461538462) equal to 0.523133481 and -0.523133481.Subproblem 1
n + 0.3461538462 = 0.523133481 Simplifying n + 0.3461538462 = 0.523133481 Reorder the terms: 0.3461538462 + n = 0.523133481 Solving 0.3461538462 + n = 0.523133481 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.3461538462' to each side of the equation. 0.3461538462 + -0.3461538462 + n = 0.523133481 + -0.3461538462 Combine like terms: 0.3461538462 + -0.3461538462 = 0.0000000000 0.0000000000 + n = 0.523133481 + -0.3461538462 n = 0.523133481 + -0.3461538462 Combine like terms: 0.523133481 + -0.3461538462 = 0.1769796348 n = 0.1769796348 Simplifying n = 0.1769796348Subproblem 2
n + 0.3461538462 = -0.523133481 Simplifying n + 0.3461538462 = -0.523133481 Reorder the terms: 0.3461538462 + n = -0.523133481 Solving 0.3461538462 + n = -0.523133481 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.3461538462' to each side of the equation. 0.3461538462 + -0.3461538462 + n = -0.523133481 + -0.3461538462 Combine like terms: 0.3461538462 + -0.3461538462 = 0.0000000000 0.0000000000 + n = -0.523133481 + -0.3461538462 n = -0.523133481 + -0.3461538462 Combine like terms: -0.523133481 + -0.3461538462 = -0.8692873272 n = -0.8692873272 Simplifying n = -0.8692873272Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.1769796348, -0.8692873272}
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