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Simplifying 7n2 + -1n + -15 = 4 Reorder the terms: -15 + -1n + 7n2 = 4 Solving -15 + -1n + 7n2 = 4 Solving for variable 'n'. Reorder the terms: -15 + -4 + -1n + 7n2 = 4 + -4 Combine like terms: -15 + -4 = -19 -19 + -1n + 7n2 = 4 + -4 Combine like terms: 4 + -4 = 0 -19 + -1n + 7n2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -2.714285714 + -0.1428571429n + n2 = 0 Move the constant term to the right: Add '2.714285714' to each side of the equation. -2.714285714 + -0.1428571429n + 2.714285714 + n2 = 0 + 2.714285714 Reorder the terms: -2.714285714 + 2.714285714 + -0.1428571429n + n2 = 0 + 2.714285714 Combine like terms: -2.714285714 + 2.714285714 = 0.000000000 0.000000000 + -0.1428571429n + n2 = 0 + 2.714285714 -0.1428571429n + n2 = 0 + 2.714285714 Combine like terms: 0 + 2.714285714 = 2.714285714 -0.1428571429n + n2 = 2.714285714 The n term is -0.1428571429n. Take half its coefficient (-0.07142857145). Square it (0.005102040819) and add it to both sides. Add '0.005102040819' to each side of the equation. -0.1428571429n + 0.005102040819 + n2 = 2.714285714 + 0.005102040819 Reorder the terms: 0.005102040819 + -0.1428571429n + n2 = 2.714285714 + 0.005102040819 Combine like terms: 2.714285714 + 0.005102040819 = 2.719387754819 0.005102040819 + -0.1428571429n + n2 = 2.719387754819 Factor a perfect square on the left side: (n + -0.07142857145)(n + -0.07142857145) = 2.719387754819 Calculate the square root of the right side: 1.649056626 Break this problem into two subproblems by setting (n + -0.07142857145) equal to 1.649056626 and -1.649056626.Subproblem 1
n + -0.07142857145 = 1.649056626 Simplifying n + -0.07142857145 = 1.649056626 Reorder the terms: -0.07142857145 + n = 1.649056626 Solving -0.07142857145 + n = 1.649056626 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.07142857145' to each side of the equation. -0.07142857145 + 0.07142857145 + n = 1.649056626 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + n = 1.649056626 + 0.07142857145 n = 1.649056626 + 0.07142857145 Combine like terms: 1.649056626 + 0.07142857145 = 1.72048519745 n = 1.72048519745 Simplifying n = 1.72048519745Subproblem 2
n + -0.07142857145 = -1.649056626 Simplifying n + -0.07142857145 = -1.649056626 Reorder the terms: -0.07142857145 + n = -1.649056626 Solving -0.07142857145 + n = -1.649056626 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.07142857145' to each side of the equation. -0.07142857145 + 0.07142857145 + n = -1.649056626 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + n = -1.649056626 + 0.07142857145 n = -1.649056626 + 0.07142857145 Combine like terms: -1.649056626 + 0.07142857145 = -1.57762805455 n = -1.57762805455 Simplifying n = -1.57762805455Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.72048519745, -1.57762805455}
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