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Simplifying 6n2 = 10n + -3 Reorder the terms: 6n2 = -3 + 10n Solving 6n2 = -3 + 10n Solving for variable 'n'. Reorder the terms: 3 + -10n + 6n2 = -3 + 10n + 3 + -10n Reorder the terms: 3 + -10n + 6n2 = -3 + 3 + 10n + -10n Combine like terms: -3 + 3 = 0 3 + -10n + 6n2 = 0 + 10n + -10n 3 + -10n + 6n2 = 10n + -10n Combine like terms: 10n + -10n = 0 3 + -10n + 6n2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.5 + -1.666666667n + n2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -1.666666667n + -0.5 + n2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -1.666666667n + n2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -1.666666667n + n2 = 0 + -0.5 -1.666666667n + n2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -1.666666667n + n2 = -0.5 The n term is -1.666666667n. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667n + 0.6944444447 + n2 = -0.5 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667n + n2 = -0.5 + 0.6944444447 Combine like terms: -0.5 + 0.6944444447 = 0.1944444447 0.6944444447 + -1.666666667n + n2 = 0.1944444447 Factor a perfect square on the left side: (n + -0.8333333335)(n + -0.8333333335) = 0.1944444447 Calculate the square root of the right side: 0.440958552 Break this problem into two subproblems by setting (n + -0.8333333335) equal to 0.440958552 and -0.440958552.Subproblem 1
n + -0.8333333335 = 0.440958552 Simplifying n + -0.8333333335 = 0.440958552 Reorder the terms: -0.8333333335 + n = 0.440958552 Solving -0.8333333335 + n = 0.440958552 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + n = 0.440958552 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + n = 0.440958552 + 0.8333333335 n = 0.440958552 + 0.8333333335 Combine like terms: 0.440958552 + 0.8333333335 = 1.2742918855 n = 1.2742918855 Simplifying n = 1.2742918855Subproblem 2
n + -0.8333333335 = -0.440958552 Simplifying n + -0.8333333335 = -0.440958552 Reorder the terms: -0.8333333335 + n = -0.440958552 Solving -0.8333333335 + n = -0.440958552 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + n = -0.440958552 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + n = -0.440958552 + 0.8333333335 n = -0.440958552 + 0.8333333335 Combine like terms: -0.440958552 + 0.8333333335 = 0.3923747815 n = 0.3923747815 Simplifying n = 0.3923747815Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.2742918855, 0.3923747815}
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