4.9n^2+15n-44=0

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Solution for 4.9n^2+15n-44=0 equation:


Simplifying
4.9n2 + 15n + -44 = 0

Reorder the terms:
-44 + 15n + 4.9n2 = 0

Solving
-44 + 15n + 4.9n2 = 0

Solving for variable 'n'.

Begin completing the square.  Divide all terms by
4.9 the coefficient of the squared term: 

Divide each side by '4.9'.
-8.979591837 + 3.06122449n + n2 = 0

Move the constant term to the right:

Add '8.979591837' to each side of the equation.
-8.979591837 + 3.06122449n + 8.979591837 + n2 = 0 + 8.979591837

Reorder the terms:
-8.979591837 + 8.979591837 + 3.06122449n + n2 = 0 + 8.979591837

Combine like terms: -8.979591837 + 8.979591837 = 0.000000000
0.000000000 + 3.06122449n + n2 = 0 + 8.979591837
3.06122449n + n2 = 0 + 8.979591837

Combine like terms: 0 + 8.979591837 = 8.979591837
3.06122449n + n2 = 8.979591837

The n term is 3.06122449n.  Take half its coefficient (1.530612245).
Square it (2.342773845) and add it to both sides.

Add '2.342773845' to each side of the equation.
3.06122449n + 2.342773845 + n2 = 8.979591837 + 2.342773845

Reorder the terms:
2.342773845 + 3.06122449n + n2 = 8.979591837 + 2.342773845

Combine like terms: 8.979591837 + 2.342773845 = 11.322365682
2.342773845 + 3.06122449n + n2 = 11.322365682

Factor a perfect square on the left side:
(n + 1.530612245)(n + 1.530612245) = 11.322365682

Calculate the square root of the right side: 3.364872313

Break this problem into two subproblems by setting 
(n + 1.530612245) equal to 3.364872313 and -3.364872313.

Subproblem 1

n + 1.530612245 = 3.364872313 Simplifying n + 1.530612245 = 3.364872313 Reorder the terms: 1.530612245 + n = 3.364872313 Solving 1.530612245 + n = 3.364872313 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1.530612245' to each side of the equation. 1.530612245 + -1.530612245 + n = 3.364872313 + -1.530612245 Combine like terms: 1.530612245 + -1.530612245 = 0.000000000 0.000000000 + n = 3.364872313 + -1.530612245 n = 3.364872313 + -1.530612245 Combine like terms: 3.364872313 + -1.530612245 = 1.834260068 n = 1.834260068 Simplifying n = 1.834260068

Subproblem 2

n + 1.530612245 = -3.364872313 Simplifying n + 1.530612245 = -3.364872313 Reorder the terms: 1.530612245 + n = -3.364872313 Solving 1.530612245 + n = -3.364872313 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1.530612245' to each side of the equation. 1.530612245 + -1.530612245 + n = -3.364872313 + -1.530612245 Combine like terms: 1.530612245 + -1.530612245 = 0.000000000 0.000000000 + n = -3.364872313 + -1.530612245 n = -3.364872313 + -1.530612245 Combine like terms: -3.364872313 + -1.530612245 = -4.895484558 n = -4.895484558 Simplifying n = -4.895484558

Solution

The solution to the problem is based on the solutions from the subproblems. n = {1.834260068, -4.895484558}

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