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Simplifying 5n2 + -3n + -15 = 0 Reorder the terms: -15 + -3n + 5n2 = 0 Solving -15 + -3n + 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 + -0.6n + n2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -0.6n + 3 + n2 = 0 + 3 Reorder the terms: -3 + 3 + -0.6n + n2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -0.6n + n2 = 0 + 3 -0.6n + n2 = 0 + 3 Combine like terms: 0 + 3 = 3 -0.6n + n2 = 3 The n term is -0.6n. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6n + 0.09 + n2 = 3 + 0.09 Reorder the terms: 0.09 + -0.6n + n2 = 3 + 0.09 Combine like terms: 3 + 0.09 = 3.09 0.09 + -0.6n + n2 = 3.09 Factor a perfect square on the left side: (n + -0.3)(n + -0.3) = 3.09 Calculate the square root of the right side: 1.757839583 Break this problem into two subproblems by setting (n + -0.3) equal to 1.757839583 and -1.757839583.Subproblem 1
n + -0.3 = 1.757839583 Simplifying n + -0.3 = 1.757839583 Reorder the terms: -0.3 + n = 1.757839583 Solving -0.3 + n = 1.757839583 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + n = 1.757839583 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + n = 1.757839583 + 0.3 n = 1.757839583 + 0.3 Combine like terms: 1.757839583 + 0.3 = 2.057839583 n = 2.057839583 Simplifying n = 2.057839583Subproblem 2
n + -0.3 = -1.757839583 Simplifying n + -0.3 = -1.757839583 Reorder the terms: -0.3 + n = -1.757839583 Solving -0.3 + n = -1.757839583 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + n = -1.757839583 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + n = -1.757839583 + 0.3 n = -1.757839583 + 0.3 Combine like terms: -1.757839583 + 0.3 = -1.457839583 n = -1.457839583 Simplifying n = -1.457839583Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.057839583, -1.457839583}
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