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Simplifying -0.36n2 + 0.6n + -0.25 = 0 Reorder the terms: -0.25 + 0.6n + -0.36n2 = 0 Solving -0.25 + 0.6n + -0.36n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by -0.36 the coefficient of the squared term: Divide each side by '-0.36'. 0.6944444444 + -1.666666667n + n2 = 0 Move the constant term to the right: Add '-0.6944444444' to each side of the equation. 0.6944444444 + -1.666666667n + -0.6944444444 + n2 = 0 + -0.6944444444 Reorder the terms: 0.6944444444 + -0.6944444444 + -1.666666667n + n2 = 0 + -0.6944444444 Combine like terms: 0.6944444444 + -0.6944444444 = 0.0000000000 0.0000000000 + -1.666666667n + n2 = 0 + -0.6944444444 -1.666666667n + n2 = 0 + -0.6944444444 Combine like terms: 0 + -0.6944444444 = -0.6944444444 -1.666666667n + n2 = -0.6944444444 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 = -0.6944444444 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667n + n2 = -0.6944444444 + 0.6944444447 Combine like terms: -0.6944444444 + 0.6944444447 = 0.0000000003 0.6944444447 + -1.666666667n + n2 = 0.0000000003 Factor a perfect square on the left side: (n + -0.8333333335)(n + -0.8333333335) = 0.0000000003 Calculate the square root of the right side: 0.000017321 Break this problem into two subproblems by setting (n + -0.8333333335) equal to 0.000017321 and -0.000017321.Subproblem 1
n + -0.8333333335 = 0.000017321 Simplifying n + -0.8333333335 = 0.000017321 Reorder the terms: -0.8333333335 + n = 0.000017321 Solving -0.8333333335 + n = 0.000017321 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 = 0.000017321 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + n = 0.000017321 + 0.8333333335 n = 0.000017321 + 0.8333333335 Combine like terms: 0.000017321 + 0.8333333335 = 0.8333506545 n = 0.8333506545 Simplifying n = 0.8333506545Subproblem 2
n + -0.8333333335 = -0.000017321 Simplifying n + -0.8333333335 = -0.000017321 Reorder the terms: -0.8333333335 + n = -0.000017321 Solving -0.8333333335 + n = -0.000017321 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 = -0.000017321 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + n = -0.000017321 + 0.8333333335 n = -0.000017321 + 0.8333333335 Combine like terms: -0.000017321 + 0.8333333335 = 0.8333160125 n = 0.8333160125 Simplifying n = 0.8333160125Solution
The solution to the problem is based on the solutions from the subproblems. n = {0.8333506545, 0.8333160125}
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