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Simplifying 5n2 + -2n = 20 Reorder the terms: -2n + 5n2 = 20 Solving -2n + 5n2 = 20 Solving for variable 'n'. Reorder the terms: -20 + -2n + 5n2 = 20 + -20 Combine like terms: 20 + -20 = 0 -20 + -2n + 5n2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4 + -0.4n + n2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -0.4n + 4 + n2 = 0 + 4 Reorder the terms: -4 + 4 + -0.4n + n2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -0.4n + n2 = 0 + 4 -0.4n + n2 = 0 + 4 Combine like terms: 0 + 4 = 4 -0.4n + n2 = 4 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 = 4 + 0.04 Reorder the terms: 0.04 + -0.4n + n2 = 4 + 0.04 Combine like terms: 4 + 0.04 = 4.04 0.04 + -0.4n + n2 = 4.04 Factor a perfect square on the left side: (n + -0.2)(n + -0.2) = 4.04 Calculate the square root of the right side: 2.009975124 Break this problem into two subproblems by setting (n + -0.2) equal to 2.009975124 and -2.009975124.Subproblem 1
n + -0.2 = 2.009975124 Simplifying n + -0.2 = 2.009975124 Reorder the terms: -0.2 + n = 2.009975124 Solving -0.2 + n = 2.009975124 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 = 2.009975124 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + n = 2.009975124 + 0.2 n = 2.009975124 + 0.2 Combine like terms: 2.009975124 + 0.2 = 2.209975124 n = 2.209975124 Simplifying n = 2.209975124Subproblem 2
n + -0.2 = -2.009975124 Simplifying n + -0.2 = -2.009975124 Reorder the terms: -0.2 + n = -2.009975124 Solving -0.2 + n = -2.009975124 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 = -2.009975124 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + n = -2.009975124 + 0.2 n = -2.009975124 + 0.2 Combine like terms: -2.009975124 + 0.2 = -1.809975124 n = -1.809975124 Simplifying n = -1.809975124Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.209975124, -1.809975124}
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