2[w(w+18)]=72

Simple and best practice solution for 2[w(w+18)]=72 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 2[w(w+18)]=72 equation: 


Simplifying
2[w(w + 18)] = 72

Reorder the terms:
2[w(18 + w)] = 72
2[(18 * w + w * w)] = 72
2[(18w + w2)] = 72
[18w * 2 + w2 * 2] = 72
[36w + 2w2] = 72

Solving
36w + 2w2 = 72

Solving for variable 'w'.

Reorder the terms:
-72 + 36w + 2w2 = 72 + -72

Combine like terms: 72 + -72 = 0
-72 + 36w + 2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-36 + 18w + w2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-36 + 18w + w2)' equal to zero and attempt to solve:

Simplifying
-36 + 18w + w2 = 0

Solving
-36 + 18w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + 18w + 36 + w2 = 0 + 36

Reorder the terms:
-36 + 36 + 18w + w2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + 18w + w2 = 0 + 36
18w + w2 = 0 + 36

Combine like terms: 0 + 36 = 36
18w + w2 = 36

The w term is 18w.  Take half its coefficient (9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
18w + 81 + w2 = 36 + 81

Reorder the terms:
81 + 18w + w2 = 36 + 81

Combine like terms: 36 + 81 = 117
81 + 18w + w2 = 117

Factor a perfect square on the left side:
(w + 9)(w + 9) = 117

Calculate the square root of the right side: 10.816653826

Break this problem into two subproblems by setting 
(w + 9) equal to 10.816653826 and -10.816653826.


Subproblem 1
w + 9 = 10.816653826

Simplifying
w + 9 = 10.816653826

Reorder the terms:
9 + w = 10.816653826

Solving
9 + w = 10.816653826

Solving for variable 'w'.

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

Add '-9' to each side of the equation.
9 + -9 + w = 10.816653826 + -9

Combine like terms: 9 + -9 = 0
0 + w = 10.816653826 + -9
w = 10.816653826 + -9

Combine like terms: 10.816653826 + -9 = 1.816653826
w = 1.816653826

Simplifying
w = 1.816653826


Subproblem 2
w + 9 = -10.816653826

Simplifying
w + 9 = -10.816653826

Reorder the terms:
9 + w = -10.816653826

Solving
9 + w = -10.816653826

Solving for variable 'w'.

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

Add '-9' to each side of the equation.
9 + -9 + w = -10.816653826 + -9

Combine like terms: 9 + -9 = 0
0 + w = -10.816653826 + -9
w = -10.816653826 + -9

Combine like terms: -10.816653826 + -9 = -19.816653826
w = -19.816653826

Simplifying
w = -19.816653826


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {1.816653826, -19.816653826}
Solution
w = {1.816653826, -19.816653826}

See similar equations:

| 3/4x=11/3 | | 9+m=-12 | | 11n+35=24 | | -5-7x=30 | | 16+2p=24 | | 125+5x=35x | | 2m-7=5m+8 | | -12-28+10x=12 | | 4m+8.50=46.50 | | 6+3p=12 | | 11+4(x+12)=47 | | 2x+x+1=13 | | 3(m+1)=-24 | | 2w^2+36w=72 | | 5n+20=105 | | 73=v/3 | | x^2+4x+12=16x-24 | | -f-18=7 | | 44/12=9/12x | | 4(s-9)=8 | | 80-2p=20 | | p(1)=0.03+(1-.03).04 | | -x-17=20 | | -3r+15=4 | | 12y-45=3y | | 1-3r=16 | | n+23=2 | | -32=4-8-5r | | 4(k+10)=24 | | -8+10n=12 | | t/3-11=-6 | | 25+0.05x=40+0.03x |

Equations solver categories