5n^2-45n+11=0

Simple and best practice solution for 5n^2-45n+11=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 5n^2-45n+11=0 equation:


Simplifying
5n2 + -45n + 11 = 0

Reorder the terms:
11 + -45n + 5n2 = 0

Solving
11 + -45n + 5n2 = 0

Solving for variable 'n'.

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

Divide each side by '5'.
2.2 + -9n + n2 = 0

Move the constant term to the right:

Add '-2.2' to each side of the equation.
2.2 + -9n + -2.2 + n2 = 0 + -2.2

Reorder the terms:
2.2 + -2.2 + -9n + n2 = 0 + -2.2

Combine like terms: 2.2 + -2.2 = 0.0
0.0 + -9n + n2 = 0 + -2.2
-9n + n2 = 0 + -2.2

Combine like terms: 0 + -2.2 = -2.2
-9n + n2 = -2.2

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 = -2.2 + 20.25

Reorder the terms:
20.25 + -9n + n2 = -2.2 + 20.25

Combine like terms: -2.2 + 20.25 = 18.05
20.25 + -9n + n2 = 18.05

Factor a perfect square on the left side:
(n + -4.5)(n + -4.5) = 18.05

Calculate the square root of the right side: 4.248529157

Break this problem into two subproblems by setting 
(n + -4.5) equal to 4.248529157 and -4.248529157.

Subproblem 1

n + -4.5 = 4.248529157 Simplifying n + -4.5 = 4.248529157 Reorder the terms: -4.5 + n = 4.248529157 Solving -4.5 + n = 4.248529157 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 = 4.248529157 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + n = 4.248529157 + 4.5 n = 4.248529157 + 4.5 Combine like terms: 4.248529157 + 4.5 = 8.748529157 n = 8.748529157 Simplifying n = 8.748529157

Subproblem 2

n + -4.5 = -4.248529157 Simplifying n + -4.5 = -4.248529157 Reorder the terms: -4.5 + n = -4.248529157 Solving -4.5 + n = -4.248529157 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 = -4.248529157 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + n = -4.248529157 + 4.5 n = -4.248529157 + 4.5 Combine like terms: -4.248529157 + 4.5 = 0.251470843 n = 0.251470843 Simplifying n = 0.251470843

Solution

The solution to the problem is based on the solutions from the subproblems. n = {8.748529157, 0.251470843}

See similar equations:

| 1+(1+2)=122 | | 18y-13y=-100-5y | | 18600x+68600x= | | 7x+4=54+3x | | (2x+7)(2x-7)=1 | | 186000x=68600x | | 5x-3=-3x+45 | | 18+2x=-10-2x | | 11x-4=4x+52 | | a^4-4a^3*b+b^2= | | 3-(x-4)=7-x | | 6-(-5b)=5b-3 | | 60-10m=-18m-4 | | 3(x+2)-2(2x-4)=38 | | 25+7=10s-7 | | 6x+12=4x+45 | | y-(y*.10)=12000 | | 12x-6=8+6x | | -r+2=20+5r | | 6v+8=-4-v | | 40a+56b= | | w^2-12w+17=0 | | 3(2g-5)=4g+13 | | r^2-5r^2+r=0 | | x+(x+12)=84 | | x-(x*.10)=12000 | | 12x-6=9y | | -t+10=-50+5t | | -t+19=-50+5t | | 8x-3=87-x | | 0.5t=-65 | | x+(x*.10)=12000 |

Equations solver categories