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Simplifying 5n2 + -9n + -9 = 2 Reorder the terms: -9 + -9n + 5n2 = 2 Solving -9 + -9n + 5n2 = 2 Solving for variable 'n'. Reorder the terms: -9 + -2 + -9n + 5n2 = 2 + -2 Combine like terms: -9 + -2 = -11 -11 + -9n + 5n2 = 2 + -2 Combine like terms: 2 + -2 = 0 -11 + -9n + 5n2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.2 + -1.8n + n2 = 0 Move the constant term to the right: Add '2.2' to each side of the equation. -2.2 + -1.8n + 2.2 + n2 = 0 + 2.2 Reorder the terms: -2.2 + 2.2 + -1.8n + n2 = 0 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + -1.8n + n2 = 0 + 2.2 -1.8n + n2 = 0 + 2.2 Combine like terms: 0 + 2.2 = 2.2 -1.8n + n2 = 2.2 The n term is -1.8n. Take half its coefficient (-0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. -1.8n + 0.81 + n2 = 2.2 + 0.81 Reorder the terms: 0.81 + -1.8n + n2 = 2.2 + 0.81 Combine like terms: 2.2 + 0.81 = 3.01 0.81 + -1.8n + n2 = 3.01 Factor a perfect square on the left side: (n + -0.9)(n + -0.9) = 3.01 Calculate the square root of the right side: 1.734935157 Break this problem into two subproblems by setting (n + -0.9) equal to 1.734935157 and -1.734935157.Subproblem 1
n + -0.9 = 1.734935157 Simplifying n + -0.9 = 1.734935157 Reorder the terms: -0.9 + n = 1.734935157 Solving -0.9 + n = 1.734935157 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + n = 1.734935157 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + n = 1.734935157 + 0.9 n = 1.734935157 + 0.9 Combine like terms: 1.734935157 + 0.9 = 2.634935157 n = 2.634935157 Simplifying n = 2.634935157Subproblem 2
n + -0.9 = -1.734935157 Simplifying n + -0.9 = -1.734935157 Reorder the terms: -0.9 + n = -1.734935157 Solving -0.9 + n = -1.734935157 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + n = -1.734935157 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + n = -1.734935157 + 0.9 n = -1.734935157 + 0.9 Combine like terms: -1.734935157 + 0.9 = -0.834935157 n = -0.834935157 Simplifying n = -0.834935157Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.634935157, -0.834935157}
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