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Simplifying 5n2 + -6n + -48 = 0 Reorder the terms: -48 + -6n + 5n2 = 0 Solving -48 + -6n + 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'. -9.6 + -1.2n + n2 = 0 Move the constant term to the right: Add '9.6' to each side of the equation. -9.6 + -1.2n + 9.6 + n2 = 0 + 9.6 Reorder the terms: -9.6 + 9.6 + -1.2n + n2 = 0 + 9.6 Combine like terms: -9.6 + 9.6 = 0.0 0.0 + -1.2n + n2 = 0 + 9.6 -1.2n + n2 = 0 + 9.6 Combine like terms: 0 + 9.6 = 9.6 -1.2n + n2 = 9.6 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 = 9.6 + 0.36 Reorder the terms: 0.36 + -1.2n + n2 = 9.6 + 0.36 Combine like terms: 9.6 + 0.36 = 9.96 0.36 + -1.2n + n2 = 9.96 Factor a perfect square on the left side: (n + -0.6)(n + -0.6) = 9.96 Calculate the square root of the right side: 3.155946768 Break this problem into two subproblems by setting (n + -0.6) equal to 3.155946768 and -3.155946768.Subproblem 1
n + -0.6 = 3.155946768 Simplifying n + -0.6 = 3.155946768 Reorder the terms: -0.6 + n = 3.155946768 Solving -0.6 + n = 3.155946768 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 = 3.155946768 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + n = 3.155946768 + 0.6 n = 3.155946768 + 0.6 Combine like terms: 3.155946768 + 0.6 = 3.755946768 n = 3.755946768 Simplifying n = 3.755946768Subproblem 2
n + -0.6 = -3.155946768 Simplifying n + -0.6 = -3.155946768 Reorder the terms: -0.6 + n = -3.155946768 Solving -0.6 + n = -3.155946768 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 = -3.155946768 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + n = -3.155946768 + 0.6 n = -3.155946768 + 0.6 Combine like terms: -3.155946768 + 0.6 = -2.555946768 n = -2.555946768 Simplifying n = -2.555946768Solution
The solution to the problem is based on the solutions from the subproblems. n = {3.755946768, -2.555946768}
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