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Simplifying 5n2 + -2n + -15 = 0 Reorder the terms: -15 + -2n + 5n2 = 0 Solving -15 + -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'. -3 + -0.4n + n2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -0.4n + 3 + n2 = 0 + 3 Reorder the terms: -3 + 3 + -0.4n + n2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -0.4n + n2 = 0 + 3 -0.4n + n2 = 0 + 3 Combine like terms: 0 + 3 = 3 -0.4n + n2 = 3 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 = 3 + 0.04 Reorder the terms: 0.04 + -0.4n + n2 = 3 + 0.04 Combine like terms: 3 + 0.04 = 3.04 0.04 + -0.4n + n2 = 3.04 Factor a perfect square on the left side: (n + -0.2)(n + -0.2) = 3.04 Calculate the square root of the right side: 1.743559577 Break this problem into two subproblems by setting (n + -0.2) equal to 1.743559577 and -1.743559577.Subproblem 1
n + -0.2 = 1.743559577 Simplifying n + -0.2 = 1.743559577 Reorder the terms: -0.2 + n = 1.743559577 Solving -0.2 + n = 1.743559577 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 = 1.743559577 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + n = 1.743559577 + 0.2 n = 1.743559577 + 0.2 Combine like terms: 1.743559577 + 0.2 = 1.943559577 n = 1.943559577 Simplifying n = 1.943559577Subproblem 2
n + -0.2 = -1.743559577 Simplifying n + -0.2 = -1.743559577 Reorder the terms: -0.2 + n = -1.743559577 Solving -0.2 + n = -1.743559577 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 = -1.743559577 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + n = -1.743559577 + 0.2 n = -1.743559577 + 0.2 Combine like terms: -1.743559577 + 0.2 = -1.543559577 n = -1.543559577 Simplifying n = -1.543559577Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.943559577, -1.543559577}
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