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Simplifying 9n2 + -5n + -42 = 0 Reorder the terms: -42 + -5n + 9n2 = 0 Solving -42 + -5n + 9n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -4.666666667 + -0.5555555556n + n2 = 0 Move the constant term to the right: Add '4.666666667' to each side of the equation. -4.666666667 + -0.5555555556n + 4.666666667 + n2 = 0 + 4.666666667 Reorder the terms: -4.666666667 + 4.666666667 + -0.5555555556n + n2 = 0 + 4.666666667 Combine like terms: -4.666666667 + 4.666666667 = 0.000000000 0.000000000 + -0.5555555556n + n2 = 0 + 4.666666667 -0.5555555556n + n2 = 0 + 4.666666667 Combine like terms: 0 + 4.666666667 = 4.666666667 -0.5555555556n + n2 = 4.666666667 The n term is -0.5555555556n. Take half its coefficient (-0.2777777778). Square it (0.07716049384) and add it to both sides. Add '0.07716049384' to each side of the equation. -0.5555555556n + 0.07716049384 + n2 = 4.666666667 + 0.07716049384 Reorder the terms: 0.07716049384 + -0.5555555556n + n2 = 4.666666667 + 0.07716049384 Combine like terms: 4.666666667 + 0.07716049384 = 4.74382716084 0.07716049384 + -0.5555555556n + n2 = 4.74382716084 Factor a perfect square on the left side: (n + -0.2777777778)(n + -0.2777777778) = 4.74382716084 Calculate the square root of the right side: 2.178032865 Break this problem into two subproblems by setting (n + -0.2777777778) equal to 2.178032865 and -2.178032865.Subproblem 1
n + -0.2777777778 = 2.178032865 Simplifying n + -0.2777777778 = 2.178032865 Reorder the terms: -0.2777777778 + n = 2.178032865 Solving -0.2777777778 + n = 2.178032865 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.2777777778' to each side of the equation. -0.2777777778 + 0.2777777778 + n = 2.178032865 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + n = 2.178032865 + 0.2777777778 n = 2.178032865 + 0.2777777778 Combine like terms: 2.178032865 + 0.2777777778 = 2.4558106428 n = 2.4558106428 Simplifying n = 2.4558106428Subproblem 2
n + -0.2777777778 = -2.178032865 Simplifying n + -0.2777777778 = -2.178032865 Reorder the terms: -0.2777777778 + n = -2.178032865 Solving -0.2777777778 + n = -2.178032865 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.2777777778' to each side of the equation. -0.2777777778 + 0.2777777778 + n = -2.178032865 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + n = -2.178032865 + 0.2777777778 n = -2.178032865 + 0.2777777778 Combine like terms: -2.178032865 + 0.2777777778 = -1.9002550872 n = -1.9002550872 Simplifying n = -1.9002550872Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.4558106428, -1.9002550872}
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