2n^2+15n-13=0

Simple and best practice solution for 2n^2+15n-13=0 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for 2n^2+15n-13=0 equation:


Simplifying
2n2 + 15n + -13 = 0

Reorder the terms:
-13 + 15n + 2n2 = 0

Solving
-13 + 15n + 2n2 = 0

Solving for variable 'n'.

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

Divide each side by '2'.
-6.5 + 7.5n + n2 = 0

Move the constant term to the right:

Add '6.5' to each side of the equation.
-6.5 + 7.5n + 6.5 + n2 = 0 + 6.5

Reorder the terms:
-6.5 + 6.5 + 7.5n + n2 = 0 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + 7.5n + n2 = 0 + 6.5
7.5n + n2 = 0 + 6.5

Combine like terms: 0 + 6.5 = 6.5
7.5n + n2 = 6.5

The n term is 7.5n.  Take half its coefficient (3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
7.5n + 14.0625 + n2 = 6.5 + 14.0625

Reorder the terms:
14.0625 + 7.5n + n2 = 6.5 + 14.0625

Combine like terms: 6.5 + 14.0625 = 20.5625
14.0625 + 7.5n + n2 = 20.5625

Factor a perfect square on the left side:
(n + 3.75)(n + 3.75) = 20.5625

Calculate the square root of the right side: 4.534589287

Break this problem into two subproblems by setting 
(n + 3.75) equal to 4.534589287 and -4.534589287.

Subproblem 1

n + 3.75 = 4.534589287 Simplifying n + 3.75 = 4.534589287 Reorder the terms: 3.75 + n = 4.534589287 Solving 3.75 + n = 4.534589287 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + n = 4.534589287 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + n = 4.534589287 + -3.75 n = 4.534589287 + -3.75 Combine like terms: 4.534589287 + -3.75 = 0.784589287 n = 0.784589287 Simplifying n = 0.784589287

Subproblem 2

n + 3.75 = -4.534589287 Simplifying n + 3.75 = -4.534589287 Reorder the terms: 3.75 + n = -4.534589287 Solving 3.75 + n = -4.534589287 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + n = -4.534589287 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + n = -4.534589287 + -3.75 n = -4.534589287 + -3.75 Combine like terms: -4.534589287 + -3.75 = -8.284589287 n = -8.284589287 Simplifying n = -8.284589287

Solution

The solution to the problem is based on the solutions from the subproblems. n = {0.784589287, -8.284589287}

See similar equations:

| 0.4*x=75000 | | a-32=29 | | 3x+14=-82 | | 4x^2-50x+486=0 | | t=16t^2+3136 | | X/2-8=6 | | 7.9+d=12 | | 12x-2=-3x+14 | | 2cos^2x+5cosx+5=0 | | -7-5x=-22 | | 6(1-x)+5=2x+3 | | -x-8+7= | | (x-4)(2x+5)= | | (5+3x)-(10x-15)=-22 | | (5+3x)-(10a-15)=-22 | | 26=g | | 6^9-x=1/36 | | 7-3+5x(6-2)= | | 7x^2-4x-6=0 | | h/-1.05=-o.36 | | -48a+8a=-48 | | t=1x+2 | | 4x^2-y^2-48x+140=0 | | 12x^4-8x+4x^2-3= | | 3x+8=8x-13 | | -4(-p-7)-2(5p-4)=12 | | -13m=5(1+4m)-2m | | x^2+y^2+2x+1=0 | | 2x+3=7x+9 | | -8(x+3)+8(5-4x)=-64 | | 12x+11y-50=0 | | -(-3r+2)-5(1+6r)=47 |

Equations solver categories