2w(w+5)=90

Simple and best practice solution for 2w(w+5)=90 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 2w(w+5)=90 equation: 


Simplifying
2w(w + 5) = 90

Reorder the terms:
2w(5 + w) = 90
(5 * 2w + w * 2w) = 90
(10w + 2w2) = 90

Solving
10w + 2w2 = 90

Solving for variable 'w'.

Reorder the terms:
-90 + 10w + 2w2 = 90 + -90

Combine like terms: 90 + -90 = 0
-90 + 10w + 2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-45 + 5w + w2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-45 + 5w + w2)' equal to zero and attempt to solve:

Simplifying
-45 + 5w + w2 = 0

Solving
-45 + 5w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '45' to each side of the equation.
-45 + 5w + 45 + w2 = 0 + 45

Reorder the terms:
-45 + 45 + 5w + w2 = 0 + 45

Combine like terms: -45 + 45 = 0
0 + 5w + w2 = 0 + 45
5w + w2 = 0 + 45

Combine like terms: 0 + 45 = 45
5w + w2 = 45

The w term is 5w.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5w + 6.25 + w2 = 45 + 6.25

Reorder the terms:
6.25 + 5w + w2 = 45 + 6.25

Combine like terms: 45 + 6.25 = 51.25
6.25 + 5w + w2 = 51.25

Factor a perfect square on the left side:
(w + 2.5)(w + 2.5) = 51.25

Calculate the square root of the right side: 7.158910532

Break this problem into two subproblems by setting 
(w + 2.5) equal to 7.158910532 and -7.158910532.


Subproblem 1
w + 2.5 = 7.158910532

Simplifying
w + 2.5 = 7.158910532

Reorder the terms:
2.5 + w = 7.158910532

Solving
2.5 + w = 7.158910532

Solving for variable 'w'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + w = 7.158910532 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + w = 7.158910532 + -2.5
w = 7.158910532 + -2.5

Combine like terms: 7.158910532 + -2.5 = 4.658910532
w = 4.658910532

Simplifying
w = 4.658910532


Subproblem 2
w + 2.5 = -7.158910532

Simplifying
w + 2.5 = -7.158910532

Reorder the terms:
2.5 + w = -7.158910532

Solving
2.5 + w = -7.158910532

Solving for variable 'w'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + w = -7.158910532 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + w = -7.158910532 + -2.5
w = -7.158910532 + -2.5

Combine like terms: -7.158910532 + -2.5 = -9.658910532
w = -9.658910532

Simplifying
w = -9.658910532


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {4.658910532, -9.658910532}
Solution
w = {4.658910532, -9.658910532}

See similar equations:

| (3x-20)=50 | | -2z-5-7z=22 | | X+(x-10)+(14-x)=240 | | 9y=6y^3 | | 4x^2+10x=3 | | 190-14x=180 | | 102(2x+12)= | | 10x-8y=8 | | 16-3G=4 | | 20-x=31 | | 6r+3(-4r+2)-3=21 | | y=60 | | 3.25(-0.1)= | | 20+1y=-y-6 | | 9x+5y=4.10 | | 2y+4=-2y-4 | | Y(y+12)=0 | | 1/5(75+83+92+85+f)=85 | | (-6i)(-6i)=36 | | 12x^3-75xy^2-16x^2y+100y^3= | | 17x+29y=5 | | 10x-2y=-28 | | 7x-5+x+3=180 | | 3.4andz= | | -8(-6n-6)=-32+32+8n | | -5y-9=-3y-13 | | 3x+5+4x+1=20 | | p=1+5n | | 2u^2-4w+48=0 | | 16-8*n=36 | | -8(-7n-6)=-32+8n | | (4a)*(5ab)= |

Equations solver categories