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Simplifying 20n + 20 = 7n2 + -1n Reorder the terms: 20 + 20n = 7n2 + -1n Reorder the terms: 20 + 20n = -1n + 7n2 Solving 20 + 20n = -1n + 7n2 Solving for variable 'n'. Combine like terms: 20n + n = 21n 20 + 21n + -7n2 = -1n + 7n2 + n + -7n2 Reorder the terms: 20 + 21n + -7n2 = -1n + n + 7n2 + -7n2 Combine like terms: -1n + n = 0 20 + 21n + -7n2 = 0 + 7n2 + -7n2 20 + 21n + -7n2 = 7n2 + -7n2 Combine like terms: 7n2 + -7n2 = 0 20 + 21n + -7n2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -2.857142857 + -3n + n2 = 0 Move the constant term to the right: Add '2.857142857' to each side of the equation. -2.857142857 + -3n + 2.857142857 + n2 = 0 + 2.857142857 Reorder the terms: -2.857142857 + 2.857142857 + -3n + n2 = 0 + 2.857142857 Combine like terms: -2.857142857 + 2.857142857 = 0.000000000 0.000000000 + -3n + n2 = 0 + 2.857142857 -3n + n2 = 0 + 2.857142857 Combine like terms: 0 + 2.857142857 = 2.857142857 -3n + n2 = 2.857142857 The n term is -3n. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3n + 2.25 + n2 = 2.857142857 + 2.25 Reorder the terms: 2.25 + -3n + n2 = 2.857142857 + 2.25 Combine like terms: 2.857142857 + 2.25 = 5.107142857 2.25 + -3n + n2 = 5.107142857 Factor a perfect square on the left side: (n + -1.5)(n + -1.5) = 5.107142857 Calculate the square root of the right side: 2.25989886 Break this problem into two subproblems by setting (n + -1.5) equal to 2.25989886 and -2.25989886.Subproblem 1
n + -1.5 = 2.25989886 Simplifying n + -1.5 = 2.25989886 Reorder the terms: -1.5 + n = 2.25989886 Solving -1.5 + n = 2.25989886 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + n = 2.25989886 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = 2.25989886 + 1.5 n = 2.25989886 + 1.5 Combine like terms: 2.25989886 + 1.5 = 3.75989886 n = 3.75989886 Simplifying n = 3.75989886Subproblem 2
n + -1.5 = -2.25989886 Simplifying n + -1.5 = -2.25989886 Reorder the terms: -1.5 + n = -2.25989886 Solving -1.5 + n = -2.25989886 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + n = -2.25989886 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = -2.25989886 + 1.5 n = -2.25989886 + 1.5 Combine like terms: -2.25989886 + 1.5 = -0.75989886 n = -0.75989886 Simplifying n = -0.75989886Solution
The solution to the problem is based on the solutions from the subproblems. n = {3.75989886, -0.75989886}
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