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Simplifying 5n2 + -9n + -2084 = 0 Reorder the terms: -2084 + -9n + 5n2 = 0 Solving -2084 + -9n + 5n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -416.8 + -1.8n + n2 = 0 Move the constant term to the right: Add '416.8' to each side of the equation. -416.8 + -1.8n + 416.8 + n2 = 0 + 416.8 Reorder the terms: -416.8 + 416.8 + -1.8n + n2 = 0 + 416.8 Combine like terms: -416.8 + 416.8 = 0.0 0.0 + -1.8n + n2 = 0 + 416.8 -1.8n + n2 = 0 + 416.8 Combine like terms: 0 + 416.8 = 416.8 -1.8n + n2 = 416.8 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 = 416.8 + 0.81 Reorder the terms: 0.81 + -1.8n + n2 = 416.8 + 0.81 Combine like terms: 416.8 + 0.81 = 417.61 0.81 + -1.8n + n2 = 417.61 Factor a perfect square on the left side: (n + -0.9)(n + -0.9) = 417.61 Calculate the square root of the right side: 20.435508313 Break this problem into two subproblems by setting (n + -0.9) equal to 20.435508313 and -20.435508313.Subproblem 1
n + -0.9 = 20.435508313 Simplifying n + -0.9 = 20.435508313 Reorder the terms: -0.9 + n = 20.435508313 Solving -0.9 + n = 20.435508313 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 = 20.435508313 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + n = 20.435508313 + 0.9 n = 20.435508313 + 0.9 Combine like terms: 20.435508313 + 0.9 = 21.335508313 n = 21.335508313 Simplifying n = 21.335508313Subproblem 2
n + -0.9 = -20.435508313 Simplifying n + -0.9 = -20.435508313 Reorder the terms: -0.9 + n = -20.435508313 Solving -0.9 + n = -20.435508313 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 = -20.435508313 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + n = -20.435508313 + 0.9 n = -20.435508313 + 0.9 Combine like terms: -20.435508313 + 0.9 = -19.535508313 n = -19.535508313 Simplifying n = -19.535508313Solution
The solution to the problem is based on the solutions from the subproblems. n = {21.335508313, -19.535508313}
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