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Simplifying 0 = n2 + -0.25n + -15 Reorder the terms: 0 = -15 + -0.25n + n2 Solving 0 = -15 + -0.25n + n2 Solving for variable 'n'. Combine like terms: 0 + 15 = 15 15 + 0.25n + -1n2 = -15 + -0.25n + n2 + 15 + 0.25n + -1n2 Reorder the terms: 15 + 0.25n + -1n2 = -15 + 15 + -0.25n + 0.25n + n2 + -1n2 Combine like terms: -15 + 15 = 0 15 + 0.25n + -1n2 = 0 + -0.25n + 0.25n + n2 + -1n2 15 + 0.25n + -1n2 = -0.25n + 0.25n + n2 + -1n2 Combine like terms: -0.25n + 0.25n = 0.00 15 + 0.25n + -1n2 = 0.00 + n2 + -1n2 15 + 0.25n + -1n2 = n2 + -1n2 Combine like terms: n2 + -1n2 = 0 15 + 0.25n + -1n2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -15 + -0.25n + n2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + -0.25n + 15 + n2 = 0 + 15 Reorder the terms: -15 + 15 + -0.25n + n2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -0.25n + n2 = 0 + 15 -0.25n + n2 = 0 + 15 Combine like terms: 0 + 15 = 15 -0.25n + n2 = 15 The n term is -0.25n. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25n + 0.015625 + n2 = 15 + 0.015625 Reorder the terms: 0.015625 + -0.25n + n2 = 15 + 0.015625 Combine like terms: 15 + 0.015625 = 15.015625 0.015625 + -0.25n + n2 = 15.015625 Factor a perfect square on the left side: (n + -0.125)(n + -0.125) = 15.015625 Calculate the square root of the right side: 3.875 Break this problem into two subproblems by setting (n + -0.125) equal to 3.875 and -3.875.Subproblem 1
n + -0.125 = 3.875 Simplifying n + -0.125 = 3.875 Reorder the terms: -0.125 + n = 3.875 Solving -0.125 + n = 3.875 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + n = 3.875 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + n = 3.875 + 0.125 n = 3.875 + 0.125 Combine like terms: 3.875 + 0.125 = 4 n = 4 Simplifying n = 4Subproblem 2
n + -0.125 = -3.875 Simplifying n + -0.125 = -3.875 Reorder the terms: -0.125 + n = -3.875 Solving -0.125 + n = -3.875 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + n = -3.875 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + n = -3.875 + 0.125 n = -3.875 + 0.125 Combine like terms: -3.875 + 0.125 = -3.75 n = -3.75 Simplifying n = -3.75Solution
The solution to the problem is based on the solutions from the subproblems. n = {4, -3.75}
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