n^2+9n-107=-8

Simple and best practice solution for n^2+9n-107=-8 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+9n-107=-8 equation:


Simplifying
n2 + 9n + -107 = -8

Reorder the terms:
-107 + 9n + n2 = -8

Solving
-107 + 9n + n2 = -8

Solving for variable 'n'.

Reorder the terms:
-107 + 8 + 9n + n2 = -8 + 8

Combine like terms: -107 + 8 = -99
-99 + 9n + n2 = -8 + 8

Combine like terms: -8 + 8 = 0
-99 + 9n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '99' to each side of the equation.
-99 + 9n + 99 + n2 = 0 + 99

Reorder the terms:
-99 + 99 + 9n + n2 = 0 + 99

Combine like terms: -99 + 99 = 0
0 + 9n + n2 = 0 + 99
9n + n2 = 0 + 99

Combine like terms: 0 + 99 = 99
9n + n2 = 99

The n term is 9n.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9n + 20.25 + n2 = 99 + 20.25

Reorder the terms:
20.25 + 9n + n2 = 99 + 20.25

Combine like terms: 99 + 20.25 = 119.25
20.25 + 9n + n2 = 119.25

Factor a perfect square on the left side:
(n + 4.5)(n + 4.5) = 119.25

Calculate the square root of the right side: 10.920164834

Break this problem into two subproblems by setting 
(n + 4.5) equal to 10.920164834 and -10.920164834.

Subproblem 1

n + 4.5 = 10.920164834 Simplifying n + 4.5 = 10.920164834 Reorder the terms: 4.5 + n = 10.920164834 Solving 4.5 + n = 10.920164834 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + n = 10.920164834 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + n = 10.920164834 + -4.5 n = 10.920164834 + -4.5 Combine like terms: 10.920164834 + -4.5 = 6.420164834 n = 6.420164834 Simplifying n = 6.420164834

Subproblem 2

n + 4.5 = -10.920164834 Simplifying n + 4.5 = -10.920164834 Reorder the terms: 4.5 + n = -10.920164834 Solving 4.5 + n = -10.920164834 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + n = -10.920164834 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + n = -10.920164834 + -4.5 n = -10.920164834 + -4.5 Combine like terms: -10.920164834 + -4.5 = -15.420164834 n = -15.420164834 Simplifying n = -15.420164834

Solution

The solution to the problem is based on the solutions from the subproblems. n = {6.420164834, -15.420164834}

See similar equations:

| -4-5r=2r+3 | | 2[5+2(-x)]=18+3(-x) | | x-2.5=-4.7 | | 3(u-3)-6=6 | | 2x-y=z | | (x-1.2)(x+1.2)=0 | | -5h-3h+11=-5 | | x^3+6x^2-49x-294=0 | | 1.2+3.7=2.2x-4.5 | | 1.9x+1.4=18.5 | | 6x+20=14x+68 | | 3(45-12)+30=x | | n^2+12n+42=7 | | 16+12r+4=24 | | 4x-6-5x=-2 | | 38x+5-3= | | n+2=8n+2 | | 10x^2-2x-2=0 | | (4x+7)(8-x)=0 | | 38x+5= | | 9y-5-3y=(y+1)-5 | | 12s+12=25 | | x+-5=5+6x | | s^2=169 | | x=-y+2 | | 3(x+5)=4(3-2x) | | y=-9x^2+144x-572 | | 7+5x= | | -(3/4)m+3=8 | | 0.5X-1.1=4.9 | | 4(4X+12)-30=6(X-2) | | 3b+2=-2 |

Equations solver categories