n^2-11n=30

Simple and best practice solution for n^2-11n=30 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^2-11n=30 equation:


Simplifying
n2 + -11n = 30

Reorder the terms:
-11n + n2 = 30

Solving
-11n + n2 = 30

Solving for variable 'n'.

Reorder the terms:
-30 + -11n + n2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + -11n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + -11n + 30 + n2 = 0 + 30

Reorder the terms:
-30 + 30 + -11n + n2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + -11n + n2 = 0 + 30
-11n + n2 = 0 + 30

Combine like terms: 0 + 30 = 30
-11n + n2 = 30

The n term is -11n.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11n + 30.25 + n2 = 30 + 30.25

Reorder the terms:
30.25 + -11n + n2 = 30 + 30.25

Combine like terms: 30 + 30.25 = 60.25
30.25 + -11n + n2 = 60.25

Factor a perfect square on the left side:
(n + -5.5)(n + -5.5) = 60.25

Calculate the square root of the right side: 7.762087348

Break this problem into two subproblems by setting 
(n + -5.5) equal to 7.762087348 and -7.762087348.

Subproblem 1

n + -5.5 = 7.762087348 Simplifying n + -5.5 = 7.762087348 Reorder the terms: -5.5 + n = 7.762087348 Solving -5.5 + n = 7.762087348 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + n = 7.762087348 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + n = 7.762087348 + 5.5 n = 7.762087348 + 5.5 Combine like terms: 7.762087348 + 5.5 = 13.262087348 n = 13.262087348 Simplifying n = 13.262087348

Subproblem 2

n + -5.5 = -7.762087348 Simplifying n + -5.5 = -7.762087348 Reorder the terms: -5.5 + n = -7.762087348 Solving -5.5 + n = -7.762087348 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + n = -7.762087348 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + n = -7.762087348 + 5.5 n = -7.762087348 + 5.5 Combine like terms: -7.762087348 + 5.5 = -2.262087348 n = -2.262087348 Simplifying n = -2.262087348

Solution

The solution to the problem is based on the solutions from the subproblems. n = {13.262087348, -2.262087348}

See similar equations:

| 12x+2+9x-6+122=180 | | 7p+6=6p+12 | | -9n=-9(-10-4n) | | 3(-1)+y=6 | | 2n^2-22n=60 | | -54-x=3x+14 | | 6v=70-4v | | -1+2(3+-7r)= | | -4m-48=36 | | -9=-9(-10-4n) | | 4y+2=7y-7 | | 3-log(x)=0 | | -3(8y-4)=3(1-9y)+11 | | -22.9-a=21.5 | | 120-75= | | 3-ln(x)=0 | | 7(10w+10)+3w= | | 3m=m+32 | | 7x+43x+8= | | -5x-37=-11x+65 | | x+2(5)=10 | | 13x+1+9x+3+70=180 | | x+2(7)=10 | | -38-5n=-5(-7n-7)+7 | | x^3+x^2+64x+64=0 | | -76-5x=20+x | | A-7=8 | | -2b-5=-17 | | y=-(-5) | | x(3+6)=108 | | w-4=w-5-3 | | 28-(-5)= |

Equations solver categories