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Simplifying 5n2 + -8n + -22 = 0 Reorder the terms: -22 + -8n + 5n2 = 0 Solving -22 + -8n + 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'. -4.4 + -1.6n + n2 = 0 Move the constant term to the right: Add '4.4' to each side of the equation. -4.4 + -1.6n + 4.4 + n2 = 0 + 4.4 Reorder the terms: -4.4 + 4.4 + -1.6n + n2 = 0 + 4.4 Combine like terms: -4.4 + 4.4 = 0.0 0.0 + -1.6n + n2 = 0 + 4.4 -1.6n + n2 = 0 + 4.4 Combine like terms: 0 + 4.4 = 4.4 -1.6n + n2 = 4.4 The n term is -1.6n. Take half its coefficient (-0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. -1.6n + 0.64 + n2 = 4.4 + 0.64 Reorder the terms: 0.64 + -1.6n + n2 = 4.4 + 0.64 Combine like terms: 4.4 + 0.64 = 5.04 0.64 + -1.6n + n2 = 5.04 Factor a perfect square on the left side: (n + -0.8)(n + -0.8) = 5.04 Calculate the square root of the right side: 2.244994432 Break this problem into two subproblems by setting (n + -0.8) equal to 2.244994432 and -2.244994432.Subproblem 1
n + -0.8 = 2.244994432 Simplifying n + -0.8 = 2.244994432 Reorder the terms: -0.8 + n = 2.244994432 Solving -0.8 + n = 2.244994432 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + n = 2.244994432 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + n = 2.244994432 + 0.8 n = 2.244994432 + 0.8 Combine like terms: 2.244994432 + 0.8 = 3.044994432 n = 3.044994432 Simplifying n = 3.044994432Subproblem 2
n + -0.8 = -2.244994432 Simplifying n + -0.8 = -2.244994432 Reorder the terms: -0.8 + n = -2.244994432 Solving -0.8 + n = -2.244994432 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + n = -2.244994432 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + n = -2.244994432 + 0.8 n = -2.244994432 + 0.8 Combine like terms: -2.244994432 + 0.8 = -1.444994432 n = -1.444994432 Simplifying n = -1.444994432Solution
The solution to the problem is based on the solutions from the subproblems. n = {3.044994432, -1.444994432}
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