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Simplifying 5n2 + -6n + -10 = 15 Reorder the terms: -10 + -6n + 5n2 = 15 Solving -10 + -6n + 5n2 = 15 Solving for variable 'n'. Reorder the terms: -10 + -15 + -6n + 5n2 = 15 + -15 Combine like terms: -10 + -15 = -25 -25 + -6n + 5n2 = 15 + -15 Combine like terms: 15 + -15 = 0 -25 + -6n + 5n2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -5 + -1.2n + n2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -1.2n + 5 + n2 = 0 + 5 Reorder the terms: -5 + 5 + -1.2n + n2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1.2n + n2 = 0 + 5 -1.2n + n2 = 0 + 5 Combine like terms: 0 + 5 = 5 -1.2n + n2 = 5 The n term is -1.2n. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2n + 0.36 + n2 = 5 + 0.36 Reorder the terms: 0.36 + -1.2n + n2 = 5 + 0.36 Combine like terms: 5 + 0.36 = 5.36 0.36 + -1.2n + n2 = 5.36 Factor a perfect square on the left side: (n + -0.6)(n + -0.6) = 5.36 Calculate the square root of the right side: 2.315167381 Break this problem into two subproblems by setting (n + -0.6) equal to 2.315167381 and -2.315167381.Subproblem 1
n + -0.6 = 2.315167381 Simplifying n + -0.6 = 2.315167381 Reorder the terms: -0.6 + n = 2.315167381 Solving -0.6 + n = 2.315167381 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + n = 2.315167381 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + n = 2.315167381 + 0.6 n = 2.315167381 + 0.6 Combine like terms: 2.315167381 + 0.6 = 2.915167381 n = 2.915167381 Simplifying n = 2.915167381Subproblem 2
n + -0.6 = -2.315167381 Simplifying n + -0.6 = -2.315167381 Reorder the terms: -0.6 + n = -2.315167381 Solving -0.6 + n = -2.315167381 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + n = -2.315167381 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + n = -2.315167381 + 0.6 n = -2.315167381 + 0.6 Combine like terms: -2.315167381 + 0.6 = -1.715167381 n = -1.715167381 Simplifying n = -1.715167381Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.915167381, -1.715167381}
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