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Simplifying 5n2 + -3n + -126 = 0 Reorder the terms: -126 + -3n + 5n2 = 0 Solving -126 + -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'. -25.2 + -0.6n + n2 = 0 Move the constant term to the right: Add '25.2' to each side of the equation. -25.2 + -0.6n + 25.2 + n2 = 0 + 25.2 Reorder the terms: -25.2 + 25.2 + -0.6n + n2 = 0 + 25.2 Combine like terms: -25.2 + 25.2 = 0.0 0.0 + -0.6n + n2 = 0 + 25.2 -0.6n + n2 = 0 + 25.2 Combine like terms: 0 + 25.2 = 25.2 -0.6n + n2 = 25.2 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 = 25.2 + 0.09 Reorder the terms: 0.09 + -0.6n + n2 = 25.2 + 0.09 Combine like terms: 25.2 + 0.09 = 25.29 0.09 + -0.6n + n2 = 25.29 Factor a perfect square on the left side: (n + -0.3)(n + -0.3) = 25.29 Calculate the square root of the right side: 5.028916384 Break this problem into two subproblems by setting (n + -0.3) equal to 5.028916384 and -5.028916384.Subproblem 1
n + -0.3 = 5.028916384 Simplifying n + -0.3 = 5.028916384 Reorder the terms: -0.3 + n = 5.028916384 Solving -0.3 + n = 5.028916384 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 = 5.028916384 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + n = 5.028916384 + 0.3 n = 5.028916384 + 0.3 Combine like terms: 5.028916384 + 0.3 = 5.328916384 n = 5.328916384 Simplifying n = 5.328916384Subproblem 2
n + -0.3 = -5.028916384 Simplifying n + -0.3 = -5.028916384 Reorder the terms: -0.3 + n = -5.028916384 Solving -0.3 + n = -5.028916384 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 = -5.028916384 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + n = -5.028916384 + 0.3 n = -5.028916384 + 0.3 Combine like terms: -5.028916384 + 0.3 = -4.728916384 n = -4.728916384 Simplifying n = -4.728916384Solution
The solution to the problem is based on the solutions from the subproblems. n = {5.328916384, -4.728916384}
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