16s^2+72s+18=0

Simple and best practice solution for 16s^2+72s+18=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 16s^2+72s+18=0 equation: 


Simplifying
16s2 + 72s + 18 = 0

Reorder the terms:
18 + 72s + 16s2 = 0

Solving
18 + 72s + 16s2 = 0

Solving for variable 's'.

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + 36s + 8s2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(9 + 36s + 8s2)' equal to zero and attempt to solve:

Simplifying
9 + 36s + 8s2 = 0

Solving
9 + 36s + 8s2 = 0

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

Divide each side by '8'.
1.125 + 4.5s + s2 = 0

Move the constant term to the right:

Add '-1.125' to each side of the equation.
1.125 + 4.5s + -1.125 + s2 = 0 + -1.125

Reorder the terms:
1.125 + -1.125 + 4.5s + s2 = 0 + -1.125

Combine like terms: 1.125 + -1.125 = 0.000
0.000 + 4.5s + s2 = 0 + -1.125
4.5s + s2 = 0 + -1.125

Combine like terms: 0 + -1.125 = -1.125
4.5s + s2 = -1.125

The s term is 4.5s.  Take half its coefficient (2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
4.5s + 5.0625 + s2 = -1.125 + 5.0625

Reorder the terms:
5.0625 + 4.5s + s2 = -1.125 + 5.0625

Combine like terms: -1.125 + 5.0625 = 3.9375
5.0625 + 4.5s + s2 = 3.9375

Factor a perfect square on the left side:
(s + 2.25)(s + 2.25) = 3.9375

Calculate the square root of the right side: 1.984313483

Break this problem into two subproblems by setting 
(s + 2.25) equal to 1.984313483 and -1.984313483.


Subproblem 1
s + 2.25 = 1.984313483

Simplifying
s + 2.25 = 1.984313483

Reorder the terms:
2.25 + s = 1.984313483

Solving
2.25 + s = 1.984313483

Solving for variable 's'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + s = 1.984313483 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + s = 1.984313483 + -2.25
s = 1.984313483 + -2.25

Combine like terms: 1.984313483 + -2.25 = -0.265686517
s = -0.265686517

Simplifying
s = -0.265686517


Subproblem 2
s + 2.25 = -1.984313483

Simplifying
s + 2.25 = -1.984313483

Reorder the terms:
2.25 + s = -1.984313483

Solving
2.25 + s = -1.984313483

Solving for variable 's'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + s = -1.984313483 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + s = -1.984313483 + -2.25
s = -1.984313483 + -2.25

Combine like terms: -1.984313483 + -2.25 = -4.234313483
s = -4.234313483

Simplifying
s = -4.234313483


Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {-0.265686517, -4.234313483}
Solution
s = {-0.265686517, -4.234313483}

See similar equations:

| 12(-82x+26)=84(2x+62) | | 5/3x=56 | | x+5/3=56 | | 4c^2-36c=0 | | 9(3x+6)+(x+2)=11 | | 2n(8n+1)=0 | | 9x+90+y=180 | | x(-5x+2)=24 | | -3u-w=u+7w | | 4x+8+5x-7=180 | | 12+6x=42 | | 6=t+7s | | 6(t-3)+6t=4(3t+5)-12 | | 5x-9x+8=-2+6 | | -2+3x=12 | | -6z-6=-12z+12 | | 9x-6+6x-1+82=180 | | ((-2w^2)/(v^4))^3 | | 5(-2)-2x=20 | | 1/40*n=60 | | 8x^2+21x-28=0 | | 5y+4x=20 | | 1/40*x100=60 | | 2/10x=10 | | x+2=x^2+3x-4 | | x-8.3=-4.5 | | x+2=x^2+2x-4 | | 4x^6-4x^5-8x^4-9x^2+9x+18=0 | | p+37=15 | | 4n+7n=20 | | 2*n=327 | | 0=-1/2x+4 |

Equations solver categories