2n^2-30n+10=0

Simple and best practice solution for 2n^2-30n+10=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^2-30n+10=0 equation: 


Simplifying
2n2 + -30n + 10 = 0

Reorder the terms:
10 + -30n + 2n2 = 0

Solving
10 + -30n + 2n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + -15n + n2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(5 + -15n + n2)' equal to zero and attempt to solve:

Simplifying
5 + -15n + n2 = 0

Solving
5 + -15n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -15n + -5 + n2 = 0 + -5

Reorder the terms:
5 + -5 + -15n + n2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -15n + n2 = 0 + -5
-15n + n2 = 0 + -5

Combine like terms: 0 + -5 = -5
-15n + n2 = -5

The n term is -15n.  Take half its coefficient (-7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
-15n + 56.25 + n2 = -5 + 56.25

Reorder the terms:
56.25 + -15n + n2 = -5 + 56.25

Combine like terms: -5 + 56.25 = 51.25
56.25 + -15n + n2 = 51.25

Factor a perfect square on the left side:
(n + -7.5)(n + -7.5) = 51.25

Calculate the square root of the right side: 7.158910532

Break this problem into two subproblems by setting 
(n + -7.5) equal to 7.158910532 and -7.158910532.


Subproblem 1
n + -7.5 = 7.158910532

Simplifying
n + -7.5 = 7.158910532

Reorder the terms:
-7.5 + n = 7.158910532

Solving
-7.5 + n = 7.158910532

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '7.5' to each side of the equation.
-7.5 + 7.5 + n = 7.158910532 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + n = 7.158910532 + 7.5
n = 7.158910532 + 7.5

Combine like terms: 7.158910532 + 7.5 = 14.658910532
n = 14.658910532

Simplifying
n = 14.658910532


Subproblem 2
n + -7.5 = -7.158910532

Simplifying
n + -7.5 = -7.158910532

Reorder the terms:
-7.5 + n = -7.158910532

Solving
-7.5 + n = -7.158910532

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '7.5' to each side of the equation.
-7.5 + 7.5 + n = -7.158910532 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + n = -7.158910532 + 7.5
n = -7.158910532 + 7.5

Combine like terms: -7.158910532 + 7.5 = 0.341089468
n = 0.341089468

Simplifying
n = 0.341089468


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {14.658910532, 0.341089468}
Solution
n = {14.658910532, 0.341089468}

See similar equations:

| 2x+4.5=10 | | Ab-12=20 | | X-23=53+5x | | 27=x3/4 | | -t+12=16-3t | | 284+10x-4=360 | | -94+7x=101-6x | | 3x/2=13 | | 4+6x+4=8 | | 4x+13=-2x-19 | | 9x+21=11 | | -94=101-6x | | 3x=2+12 | | 4x+13=4x-19 | | 284+25x+1=360 | | 21f+2=19f+22 | | log(x+132)+(logx+2)=logx | | -x-89=5x+43 | | (5b+3)(b-1)=0 | | 10x+12y=520 | | -29-8x=43-11x | | 2h+15=9 | | 2h+15=19 | | 2r+8=4 | | 3/7×13 | | 2(x+4)=4c-1 | | 49x^4-x^2-49x^2y^2+y^2=0 | | 7x+12=-8x-18 | | 4j-7=28 | | -7x+10x=9x+15 | | 5(x-3)=5x-9 | | 3y+7x=108 |

Equations solver categories