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Simplifying 18n2 + -1n + -4 = 87 Reorder the terms: -4 + -1n + 18n2 = 87 Solving -4 + -1n + 18n2 = 87 Solving for variable 'n'. Reorder the terms: -4 + -87 + -1n + 18n2 = 87 + -87 Combine like terms: -4 + -87 = -91 -91 + -1n + 18n2 = 87 + -87 Combine like terms: 87 + -87 = 0 -91 + -1n + 18n2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -5.055555556 + -0.05555555556n + n2 = 0 Move the constant term to the right: Add '5.055555556' to each side of the equation. -5.055555556 + -0.05555555556n + 5.055555556 + n2 = 0 + 5.055555556 Reorder the terms: -5.055555556 + 5.055555556 + -0.05555555556n + n2 = 0 + 5.055555556 Combine like terms: -5.055555556 + 5.055555556 = 0.000000000 0.000000000 + -0.05555555556n + n2 = 0 + 5.055555556 -0.05555555556n + n2 = 0 + 5.055555556 Combine like terms: 0 + 5.055555556 = 5.055555556 -0.05555555556n + n2 = 5.055555556 The n term is -0.05555555556n. Take half its coefficient (-0.02777777778). Square it (0.0007716049384) and add it to both sides. Add '0.0007716049384' to each side of the equation. -0.05555555556n + 0.0007716049384 + n2 = 5.055555556 + 0.0007716049384 Reorder the terms: 0.0007716049384 + -0.05555555556n + n2 = 5.055555556 + 0.0007716049384 Combine like terms: 5.055555556 + 0.0007716049384 = 5.0563271609384 0.0007716049384 + -0.05555555556n + n2 = 5.0563271609384 Factor a perfect square on the left side: (n + -0.02777777778)(n + -0.02777777778) = 5.0563271609384 Calculate the square root of the right side: 2.24862784 Break this problem into two subproblems by setting (n + -0.02777777778) equal to 2.24862784 and -2.24862784.Subproblem 1
n + -0.02777777778 = 2.24862784 Simplifying n + -0.02777777778 = 2.24862784 Reorder the terms: -0.02777777778 + n = 2.24862784 Solving -0.02777777778 + n = 2.24862784 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.02777777778' to each side of the equation. -0.02777777778 + 0.02777777778 + n = 2.24862784 + 0.02777777778 Combine like terms: -0.02777777778 + 0.02777777778 = 0.00000000000 0.00000000000 + n = 2.24862784 + 0.02777777778 n = 2.24862784 + 0.02777777778 Combine like terms: 2.24862784 + 0.02777777778 = 2.27640561778 n = 2.27640561778 Simplifying n = 2.27640561778Subproblem 2
n + -0.02777777778 = -2.24862784 Simplifying n + -0.02777777778 = -2.24862784 Reorder the terms: -0.02777777778 + n = -2.24862784 Solving -0.02777777778 + n = -2.24862784 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.02777777778' to each side of the equation. -0.02777777778 + 0.02777777778 + n = -2.24862784 + 0.02777777778 Combine like terms: -0.02777777778 + 0.02777777778 = 0.00000000000 0.00000000000 + n = -2.24862784 + 0.02777777778 n = -2.24862784 + 0.02777777778 Combine like terms: -2.24862784 + 0.02777777778 = -2.22085006222 n = -2.22085006222 Simplifying n = -2.22085006222Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.27640561778, -2.22085006222}
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