n^2+5n-65=0

Simple and best practice solution for n^2+5n-65=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 n^2+5n-65=0 equation:


Simplifying
n2 + 5n + -65 = 0

Reorder the terms:
-65 + 5n + n2 = 0

Solving
-65 + 5n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '65' to each side of the equation.
-65 + 5n + 65 + n2 = 0 + 65

Reorder the terms:
-65 + 65 + 5n + n2 = 0 + 65

Combine like terms: -65 + 65 = 0
0 + 5n + n2 = 0 + 65
5n + n2 = 0 + 65

Combine like terms: 0 + 65 = 65
5n + n2 = 65

The n term is 5n.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5n + 6.25 + n2 = 65 + 6.25

Reorder the terms:
6.25 + 5n + n2 = 65 + 6.25

Combine like terms: 65 + 6.25 = 71.25
6.25 + 5n + n2 = 71.25

Factor a perfect square on the left side:
(n + 2.5)(n + 2.5) = 71.25

Calculate the square root of the right side: 8.440971508

Break this problem into two subproblems by setting 
(n + 2.5) equal to 8.440971508 and -8.440971508.

Subproblem 1

n + 2.5 = 8.440971508 Simplifying n + 2.5 = 8.440971508 Reorder the terms: 2.5 + n = 8.440971508 Solving 2.5 + n = 8.440971508 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + n = 8.440971508 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + n = 8.440971508 + -2.5 n = 8.440971508 + -2.5 Combine like terms: 8.440971508 + -2.5 = 5.940971508 n = 5.940971508 Simplifying n = 5.940971508

Subproblem 2

n + 2.5 = -8.440971508 Simplifying n + 2.5 = -8.440971508 Reorder the terms: 2.5 + n = -8.440971508 Solving 2.5 + n = -8.440971508 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + n = -8.440971508 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + n = -8.440971508 + -2.5 n = -8.440971508 + -2.5 Combine like terms: -8.440971508 + -2.5 = -10.940971508 n = -10.940971508 Simplifying n = -10.940971508

Solution

The solution to the problem is based on the solutions from the subproblems. n = {5.940971508, -10.940971508}

See similar equations:

| 10x+14x=x | | 32x+43=19x+30 | | 5(x-6)=-40 | | 1-x=-2 | | -(A-3)=4a-3 | | -4x-5=10x+23 | | 10x+14x= | | 27x+23=32x+33 | | 39x+33=40x+29 | | 9=-9a | | 10=-5x+20 | | 20x+9=31x-2 | | 27x=14 | | -3(r+7)=-53 | | 10(x-2)=5x | | -x+32=-4x+17 | | -9x+3y=24 | | 20x-2=32x+22 | | 11p=11 | | -3x-2y=2 | | 16x+17=17x+26 | | x+20=-4 | | n^2+5n-139=0 | | 2x^2+5x-2=66 | | 3x+6=2x-4 | | -5(4x-2)=20x+10 | | 4(y+8)-7y=15 | | x^2+7xy+4x+28y=0 | | 2x+30=66 | | 2x+6z-y=7 | | 1/2(x-8)=5 | | 3-5(x+4)=10x-(x+1) |

Equations solver categories