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Simplifying 4n2 + -26n + -42 = 0 Reorder the terms: -42 + -26n + 4n2 = 0 Solving -42 + -26n + 4n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(-21 + -13n + 2n2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-21 + -13n + 2n2)' equal to zero and attempt to solve: Simplifying -21 + -13n + 2n2 = 0 Solving -21 + -13n + 2n2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -10.5 + -6.5n + n2 = 0 Move the constant term to the right: Add '10.5' to each side of the equation. -10.5 + -6.5n + 10.5 + n2 = 0 + 10.5 Reorder the terms: -10.5 + 10.5 + -6.5n + n2 = 0 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + -6.5n + n2 = 0 + 10.5 -6.5n + n2 = 0 + 10.5 Combine like terms: 0 + 10.5 = 10.5 -6.5n + n2 = 10.5 The n term is -6.5n. Take half its coefficient (-3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. -6.5n + 10.5625 + n2 = 10.5 + 10.5625 Reorder the terms: 10.5625 + -6.5n + n2 = 10.5 + 10.5625 Combine like terms: 10.5 + 10.5625 = 21.0625 10.5625 + -6.5n + n2 = 21.0625 Factor a perfect square on the left side: (n + -3.25)(n + -3.25) = 21.0625 Calculate the square root of the right side: 4.589389938 Break this problem into two subproblems by setting (n + -3.25) equal to 4.589389938 and -4.589389938.Subproblem 1
n + -3.25 = 4.589389938 Simplifying n + -3.25 = 4.589389938 Reorder the terms: -3.25 + n = 4.589389938 Solving -3.25 + n = 4.589389938 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + n = 4.589389938 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + n = 4.589389938 + 3.25 n = 4.589389938 + 3.25 Combine like terms: 4.589389938 + 3.25 = 7.839389938 n = 7.839389938 Simplifying n = 7.839389938Subproblem 2
n + -3.25 = -4.589389938 Simplifying n + -3.25 = -4.589389938 Reorder the terms: -3.25 + n = -4.589389938 Solving -3.25 + n = -4.589389938 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + n = -4.589389938 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + n = -4.589389938 + 3.25 n = -4.589389938 + 3.25 Combine like terms: -4.589389938 + 3.25 = -1.339389938 n = -1.339389938 Simplifying n = -1.339389938Solution
The solution to the problem is based on the solutions from the subproblems. n = {7.839389938, -1.339389938}Solution
n = {7.839389938, -1.339389938}
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