4n^2+6n-16=0

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Solution for 4n^2+6n-16=0 equation:


Simplifying
4n2 + 6n + -16 = 0

Reorder the terms:
-16 + 6n + 4n2 = 0

Solving
-16 + 6n + 4n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + 3n + 2n2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-8 + 3n + 2n2)' equal to zero and attempt to solve: Simplifying -8 + 3n + 2n2 = 0 Solving -8 + 3n + 2n2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -4 + 1.5n + n2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 1.5n + 4 + n2 = 0 + 4 Reorder the terms: -4 + 4 + 1.5n + n2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 1.5n + n2 = 0 + 4 1.5n + n2 = 0 + 4 Combine like terms: 0 + 4 = 4 1.5n + n2 = 4 The n term is 1.5n. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5n + 0.5625 + n2 = 4 + 0.5625 Reorder the terms: 0.5625 + 1.5n + n2 = 4 + 0.5625 Combine like terms: 4 + 0.5625 = 4.5625 0.5625 + 1.5n + n2 = 4.5625 Factor a perfect square on the left side: (n + 0.75)(n + 0.75) = 4.5625 Calculate the square root of the right side: 2.136000936 Break this problem into two subproblems by setting (n + 0.75) equal to 2.136000936 and -2.136000936.

Subproblem 1

n + 0.75 = 2.136000936 Simplifying n + 0.75 = 2.136000936 Reorder the terms: 0.75 + n = 2.136000936 Solving 0.75 + n = 2.136000936 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + n = 2.136000936 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + n = 2.136000936 + -0.75 n = 2.136000936 + -0.75 Combine like terms: 2.136000936 + -0.75 = 1.386000936 n = 1.386000936 Simplifying n = 1.386000936

Subproblem 2

n + 0.75 = -2.136000936 Simplifying n + 0.75 = -2.136000936 Reorder the terms: 0.75 + n = -2.136000936 Solving 0.75 + n = -2.136000936 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + n = -2.136000936 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + n = -2.136000936 + -0.75 n = -2.136000936 + -0.75 Combine like terms: -2.136000936 + -0.75 = -2.886000936 n = -2.886000936 Simplifying n = -2.886000936

Solution

The solution to the problem is based on the solutions from the subproblems. n = {1.386000936, -2.886000936}

Solution

n = {1.386000936, -2.886000936}

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