8n^2-24n-244=0

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Solution for 8n^2-24n-244=0 equation:


Simplifying
8n2 + -24n + -244 = 0

Reorder the terms:
-244 + -24n + 8n2 = 0

Solving
-244 + -24n + 8n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-61 + -6n + 2n2) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(-61 + -6n + 2n2)' equal to zero and attempt to solve: Simplifying -61 + -6n + 2n2 = 0 Solving -61 + -6n + 2n2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -30.5 + -3n + n2 = 0 Move the constant term to the right: Add '30.5' to each side of the equation. -30.5 + -3n + 30.5 + n2 = 0 + 30.5 Reorder the terms: -30.5 + 30.5 + -3n + n2 = 0 + 30.5 Combine like terms: -30.5 + 30.5 = 0.0 0.0 + -3n + n2 = 0 + 30.5 -3n + n2 = 0 + 30.5 Combine like terms: 0 + 30.5 = 30.5 -3n + n2 = 30.5 The n term is -3n. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3n + 2.25 + n2 = 30.5 + 2.25 Reorder the terms: 2.25 + -3n + n2 = 30.5 + 2.25 Combine like terms: 30.5 + 2.25 = 32.75 2.25 + -3n + n2 = 32.75 Factor a perfect square on the left side: (n + -1.5)(n + -1.5) = 32.75 Calculate the square root of the right side: 5.722761571 Break this problem into two subproblems by setting (n + -1.5) equal to 5.722761571 and -5.722761571.

Subproblem 1

n + -1.5 = 5.722761571 Simplifying n + -1.5 = 5.722761571 Reorder the terms: -1.5 + n = 5.722761571 Solving -1.5 + n = 5.722761571 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + n = 5.722761571 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = 5.722761571 + 1.5 n = 5.722761571 + 1.5 Combine like terms: 5.722761571 + 1.5 = 7.222761571 n = 7.222761571 Simplifying n = 7.222761571

Subproblem 2

n + -1.5 = -5.722761571 Simplifying n + -1.5 = -5.722761571 Reorder the terms: -1.5 + n = -5.722761571 Solving -1.5 + n = -5.722761571 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + n = -5.722761571 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = -5.722761571 + 1.5 n = -5.722761571 + 1.5 Combine like terms: -5.722761571 + 1.5 = -4.222761571 n = -4.222761571 Simplifying n = -4.222761571

Solution

The solution to the problem is based on the solutions from the subproblems. n = {7.222761571, -4.222761571}

Solution

n = {7.222761571, -4.222761571}

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