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Simplifying 7n2 + -10n + -3 = 0 Reorder the terms: -3 + -10n + 7n2 = 0 Solving -3 + -10n + 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'. -0.4285714286 + -1.428571429n + n2 = 0 Move the constant term to the right: Add '0.4285714286' to each side of the equation. -0.4285714286 + -1.428571429n + 0.4285714286 + n2 = 0 + 0.4285714286 Reorder the terms: -0.4285714286 + 0.4285714286 + -1.428571429n + n2 = 0 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + -1.428571429n + n2 = 0 + 0.4285714286 -1.428571429n + n2 = 0 + 0.4285714286 Combine like terms: 0 + 0.4285714286 = 0.4285714286 -1.428571429n + n2 = 0.4285714286 The n term is -1.428571429n. Take half its coefficient (-0.7142857145). Square it (0.5102040819) and add it to both sides. Add '0.5102040819' to each side of the equation. -1.428571429n + 0.5102040819 + n2 = 0.4285714286 + 0.5102040819 Reorder the terms: 0.5102040819 + -1.428571429n + n2 = 0.4285714286 + 0.5102040819 Combine like terms: 0.4285714286 + 0.5102040819 = 0.9387755105 0.5102040819 + -1.428571429n + n2 = 0.9387755105 Factor a perfect square on the left side: (n + -0.7142857145)(n + -0.7142857145) = 0.9387755105 Calculate the square root of the right side: 0.968904283 Break this problem into two subproblems by setting (n + -0.7142857145) equal to 0.968904283 and -0.968904283.Subproblem 1
n + -0.7142857145 = 0.968904283 Simplifying n + -0.7142857145 = 0.968904283 Reorder the terms: -0.7142857145 + n = 0.968904283 Solving -0.7142857145 + n = 0.968904283 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + n = 0.968904283 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + n = 0.968904283 + 0.7142857145 n = 0.968904283 + 0.7142857145 Combine like terms: 0.968904283 + 0.7142857145 = 1.6831899975 n = 1.6831899975 Simplifying n = 1.6831899975Subproblem 2
n + -0.7142857145 = -0.968904283 Simplifying n + -0.7142857145 = -0.968904283 Reorder the terms: -0.7142857145 + n = -0.968904283 Solving -0.7142857145 + n = -0.968904283 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + n = -0.968904283 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + n = -0.968904283 + 0.7142857145 n = -0.968904283 + 0.7142857145 Combine like terms: -0.968904283 + 0.7142857145 = -0.2546185685 n = -0.2546185685 Simplifying n = -0.2546185685Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.6831899975, -0.2546185685}
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