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Simplifying 7n2 + -4n = 4 Reorder the terms: -4n + 7n2 = 4 Solving -4n + 7n2 = 4 Solving for variable 'n'. Reorder the terms: -4 + -4n + 7n2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + -4n + 7n2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.5714285714 + -0.5714285714n + n2 = 0 Move the constant term to the right: Add '0.5714285714' to each side of the equation. -0.5714285714 + -0.5714285714n + 0.5714285714 + n2 = 0 + 0.5714285714 Reorder the terms: -0.5714285714 + 0.5714285714 + -0.5714285714n + n2 = 0 + 0.5714285714 Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000 0.0000000000 + -0.5714285714n + n2 = 0 + 0.5714285714 -0.5714285714n + n2 = 0 + 0.5714285714 Combine like terms: 0 + 0.5714285714 = 0.5714285714 -0.5714285714n + n2 = 0.5714285714 The n term is -0.5714285714n. Take half its coefficient (-0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. -0.5714285714n + 0.08163265305 + n2 = 0.5714285714 + 0.08163265305 Reorder the terms: 0.08163265305 + -0.5714285714n + n2 = 0.5714285714 + 0.08163265305 Combine like terms: 0.5714285714 + 0.08163265305 = 0.65306122445 0.08163265305 + -0.5714285714n + n2 = 0.65306122445 Factor a perfect square on the left side: (n + -0.2857142857)(n + -0.2857142857) = 0.65306122445 Calculate the square root of the right side: 0.808122036 Break this problem into two subproblems by setting (n + -0.2857142857) equal to 0.808122036 and -0.808122036.Subproblem 1
n + -0.2857142857 = 0.808122036 Simplifying n + -0.2857142857 = 0.808122036 Reorder the terms: -0.2857142857 + n = 0.808122036 Solving -0.2857142857 + n = 0.808122036 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + n = 0.808122036 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + n = 0.808122036 + 0.2857142857 n = 0.808122036 + 0.2857142857 Combine like terms: 0.808122036 + 0.2857142857 = 1.0938363217 n = 1.0938363217 Simplifying n = 1.0938363217Subproblem 2
n + -0.2857142857 = -0.808122036 Simplifying n + -0.2857142857 = -0.808122036 Reorder the terms: -0.2857142857 + n = -0.808122036 Solving -0.2857142857 + n = -0.808122036 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + n = -0.808122036 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + n = -0.808122036 + 0.2857142857 n = -0.808122036 + 0.2857142857 Combine like terms: -0.808122036 + 0.2857142857 = -0.5224077503 n = -0.5224077503 Simplifying n = -0.5224077503Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.0938363217, -0.5224077503}
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