10n^2+98n-20000=0

Simple and best practice solution for 10n^2+98n-20000=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 10n^2+98n-20000=0 equation: 


Simplifying
10n2 + 98n + -20000 = 0

Reorder the terms:
-20000 + 98n + 10n2 = 0

Solving
-20000 + 98n + 10n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-10000 + 49n + 5n2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-10000 + 49n + 5n2)' equal to zero and attempt to solve:

Simplifying
-10000 + 49n + 5n2 = 0

Solving
-10000 + 49n + 5n2 = 0

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

Divide each side by '5'.
-2000 + 9.8n + n2 = 0

Move the constant term to the right:

Add '2000' to each side of the equation.
-2000 + 9.8n + 2000 + n2 = 0 + 2000

Reorder the terms:
-2000 + 2000 + 9.8n + n2 = 0 + 2000

Combine like terms: -2000 + 2000 = 0
0 + 9.8n + n2 = 0 + 2000
9.8n + n2 = 0 + 2000

Combine like terms: 0 + 2000 = 2000
9.8n + n2 = 2000

The n term is 9.8n.  Take half its coefficient (4.9).
Square it (24.01) and add it to both sides.

Add '24.01' to each side of the equation.
9.8n + 24.01 + n2 = 2000 + 24.01

Reorder the terms:
24.01 + 9.8n + n2 = 2000 + 24.01

Combine like terms: 2000 + 24.01 = 2024.01
24.01 + 9.8n + n2 = 2024.01

Factor a perfect square on the left side:
(n + 4.9)(n + 4.9) = 2024.01

Calculate the square root of the right side: 44.988998655

Break this problem into two subproblems by setting 
(n + 4.9) equal to 44.988998655 and -44.988998655.


Subproblem 1
n + 4.9 = 44.988998655

Simplifying
n + 4.9 = 44.988998655

Reorder the terms:
4.9 + n = 44.988998655

Solving
4.9 + n = 44.988998655

Solving for variable 'n'.

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

Add '-4.9' to each side of the equation.
4.9 + -4.9 + n = 44.988998655 + -4.9

Combine like terms: 4.9 + -4.9 = 0.0
0.0 + n = 44.988998655 + -4.9
n = 44.988998655 + -4.9

Combine like terms: 44.988998655 + -4.9 = 40.088998655
n = 40.088998655

Simplifying
n = 40.088998655


Subproblem 2
n + 4.9 = -44.988998655

Simplifying
n + 4.9 = -44.988998655

Reorder the terms:
4.9 + n = -44.988998655

Solving
4.9 + n = -44.988998655

Solving for variable 'n'.

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

Add '-4.9' to each side of the equation.
4.9 + -4.9 + n = -44.988998655 + -4.9

Combine like terms: 4.9 + -4.9 = 0.0
0.0 + n = -44.988998655 + -4.9
n = -44.988998655 + -4.9

Combine like terms: -44.988998655 + -4.9 = -49.888998655
n = -49.888998655

Simplifying
n = -49.888998655


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {40.088998655, -49.888998655}
Solution
n = {40.088998655, -49.888998655}

See similar equations:

| Y/3=14/9 | | t/6-8=15 | | h(x)=3*3x-4 | | -9x[5x^2-3x-6]= | | 2.2q=8.8 | | 5x=6-2y | | 3yz-yz= | | h(t)=-16t^2+10t+6 | | 35-334=751 | | -n+4=(n+3) | | 2(-3z+3)=-30 | | x^2-7z+12= | | 7•6-9-21/7-8 | | y/5-8=22 | | x*2-7z+12= | | -99=-11p | | 6s+6=4s+12 | | 89=4v+17 | | y^4=625 | | 9x^2=81x | | 9=3(5-2d) | | 7(-5-8)=8(-8+13) | | 5s^3t^2[3s-5t^2]= | | 11x+28=4x+238 | | 11y-3y=48 | | 6s+6=8s-26 | | z^2+2z=20 | | s^2+5+6= | | (X-2)(x^2+5x-3)= | | 75+(z-1)y=90 | | 24=-6+(x-5) | | 4(p-6)=-32 |

Equations solver categories