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Simplifying 89 + 56n + -49n2 = 0 Solving 89 + 56n + -49n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by -49 the coefficient of the squared term: Divide each side by '-49'. -1.816326531 + -1.142857143n + n2 = 0 Move the constant term to the right: Add '1.816326531' to each side of the equation. -1.816326531 + -1.142857143n + 1.816326531 + n2 = 0 + 1.816326531 Reorder the terms: -1.816326531 + 1.816326531 + -1.142857143n + n2 = 0 + 1.816326531 Combine like terms: -1.816326531 + 1.816326531 = 0.000000000 0.000000000 + -1.142857143n + n2 = 0 + 1.816326531 -1.142857143n + n2 = 0 + 1.816326531 Combine like terms: 0 + 1.816326531 = 1.816326531 -1.142857143n + n2 = 1.816326531 The n term is -1.142857143n. Take half its coefficient (-0.5714285715). Square it (0.3265306123) and add it to both sides. Add '0.3265306123' to each side of the equation. -1.142857143n + 0.3265306123 + n2 = 1.816326531 + 0.3265306123 Reorder the terms: 0.3265306123 + -1.142857143n + n2 = 1.816326531 + 0.3265306123 Combine like terms: 1.816326531 + 0.3265306123 = 2.1428571433 0.3265306123 + -1.142857143n + n2 = 2.1428571433 Factor a perfect square on the left side: (n + -0.5714285715)(n + -0.5714285715) = 2.1428571433 Calculate the square root of the right side: 1.46385011 Break this problem into two subproblems by setting (n + -0.5714285715) equal to 1.46385011 and -1.46385011.Subproblem 1
n + -0.5714285715 = 1.46385011 Simplifying n + -0.5714285715 = 1.46385011 Reorder the terms: -0.5714285715 + n = 1.46385011 Solving -0.5714285715 + n = 1.46385011 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.5714285715' to each side of the equation. -0.5714285715 + 0.5714285715 + n = 1.46385011 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + n = 1.46385011 + 0.5714285715 n = 1.46385011 + 0.5714285715 Combine like terms: 1.46385011 + 0.5714285715 = 2.0352786815 n = 2.0352786815 Simplifying n = 2.0352786815Subproblem 2
n + -0.5714285715 = -1.46385011 Simplifying n + -0.5714285715 = -1.46385011 Reorder the terms: -0.5714285715 + n = -1.46385011 Solving -0.5714285715 + n = -1.46385011 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.5714285715' to each side of the equation. -0.5714285715 + 0.5714285715 + n = -1.46385011 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + n = -1.46385011 + 0.5714285715 n = -1.46385011 + 0.5714285715 Combine like terms: -1.46385011 + 0.5714285715 = -0.8924215385 n = -0.8924215385 Simplifying n = -0.8924215385Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.0352786815, -0.8924215385}
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