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Simplifying 7n2 + -12n + -5 = 0 Reorder the terms: -5 + -12n + 7n2 = 0 Solving -5 + -12n + 7n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.7142857143 + -1.714285714n + n2 = 0 Move the constant term to the right: Add '0.7142857143' to each side of the equation. -0.7142857143 + -1.714285714n + 0.7142857143 + n2 = 0 + 0.7142857143 Reorder the terms: -0.7142857143 + 0.7142857143 + -1.714285714n + n2 = 0 + 0.7142857143 Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000 0.0000000000 + -1.714285714n + n2 = 0 + 0.7142857143 -1.714285714n + n2 = 0 + 0.7142857143 Combine like terms: 0 + 0.7142857143 = 0.7142857143 -1.714285714n + n2 = 0.7142857143 The n term is -1.714285714n. Take half its coefficient (-0.857142857). Square it (0.7346938773) and add it to both sides. Add '0.7346938773' to each side of the equation. -1.714285714n + 0.7346938773 + n2 = 0.7142857143 + 0.7346938773 Reorder the terms: 0.7346938773 + -1.714285714n + n2 = 0.7142857143 + 0.7346938773 Combine like terms: 0.7142857143 + 0.7346938773 = 1.4489795916 0.7346938773 + -1.714285714n + n2 = 1.4489795916 Factor a perfect square on the left side: (n + -0.857142857)(n + -0.857142857) = 1.4489795916 Calculate the square root of the right side: 1.203735682 Break this problem into two subproblems by setting (n + -0.857142857) equal to 1.203735682 and -1.203735682.Subproblem 1
n + -0.857142857 = 1.203735682 Simplifying n + -0.857142857 = 1.203735682 Reorder the terms: -0.857142857 + n = 1.203735682 Solving -0.857142857 + n = 1.203735682 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.857142857' to each side of the equation. -0.857142857 + 0.857142857 + n = 1.203735682 + 0.857142857 Combine like terms: -0.857142857 + 0.857142857 = 0.000000000 0.000000000 + n = 1.203735682 + 0.857142857 n = 1.203735682 + 0.857142857 Combine like terms: 1.203735682 + 0.857142857 = 2.060878539 n = 2.060878539 Simplifying n = 2.060878539Subproblem 2
n + -0.857142857 = -1.203735682 Simplifying n + -0.857142857 = -1.203735682 Reorder the terms: -0.857142857 + n = -1.203735682 Solving -0.857142857 + n = -1.203735682 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.857142857' to each side of the equation. -0.857142857 + 0.857142857 + n = -1.203735682 + 0.857142857 Combine like terms: -0.857142857 + 0.857142857 = 0.000000000 0.000000000 + n = -1.203735682 + 0.857142857 n = -1.203735682 + 0.857142857 Combine like terms: -1.203735682 + 0.857142857 = -0.346592825 n = -0.346592825 Simplifying n = -0.346592825Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.060878539, -0.346592825}
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