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Simplifying 5n2 + -2n + -1000 = 0 Reorder the terms: -1000 + -2n + 5n2 = 0 Solving -1000 + -2n + 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'. -200 + -0.4n + n2 = 0 Move the constant term to the right: Add '200' to each side of the equation. -200 + -0.4n + 200 + n2 = 0 + 200 Reorder the terms: -200 + 200 + -0.4n + n2 = 0 + 200 Combine like terms: -200 + 200 = 0 0 + -0.4n + n2 = 0 + 200 -0.4n + n2 = 0 + 200 Combine like terms: 0 + 200 = 200 -0.4n + n2 = 200 The n term is -0.4n. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4n + 0.04 + n2 = 200 + 0.04 Reorder the terms: 0.04 + -0.4n + n2 = 200 + 0.04 Combine like terms: 200 + 0.04 = 200.04 0.04 + -0.4n + n2 = 200.04 Factor a perfect square on the left side: (n + -0.2)(n + -0.2) = 200.04 Calculate the square root of the right side: 14.143549767 Break this problem into two subproblems by setting (n + -0.2) equal to 14.143549767 and -14.143549767.Subproblem 1
n + -0.2 = 14.143549767 Simplifying n + -0.2 = 14.143549767 Reorder the terms: -0.2 + n = 14.143549767 Solving -0.2 + n = 14.143549767 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + n = 14.143549767 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + n = 14.143549767 + 0.2 n = 14.143549767 + 0.2 Combine like terms: 14.143549767 + 0.2 = 14.343549767 n = 14.343549767 Simplifying n = 14.343549767Subproblem 2
n + -0.2 = -14.143549767 Simplifying n + -0.2 = -14.143549767 Reorder the terms: -0.2 + n = -14.143549767 Solving -0.2 + n = -14.143549767 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + n = -14.143549767 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + n = -14.143549767 + 0.2 n = -14.143549767 + 0.2 Combine like terms: -14.143549767 + 0.2 = -13.943549767 n = -13.943549767 Simplifying n = -13.943549767Solution
The solution to the problem is based on the solutions from the subproblems. n = {14.343549767, -13.943549767}
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