2w(2w-9)+10=0

Simple and best practice solution for 2w(2w-9)+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 2w(2w-9)+10=0 equation: 


Simplifying
2w(2w + -9) + 10 = 0

Reorder the terms:
2w(-9 + 2w) + 10 = 0
(-9 * 2w + 2w * 2w) + 10 = 0
(-18w + 4w2) + 10 = 0

Reorder the terms:
10 + -18w + 4w2 = 0

Solving
10 + -18w + 4w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + -9w + 2w2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(5 + -9w + 2w2)' equal to zero and attempt to solve:

Simplifying
5 + -9w + 2w2 = 0

Solving
5 + -9w + 2w2 = 0

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

Divide each side by '2'.
2.5 + -4.5w + w2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + -4.5w + -2.5 + w2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + -4.5w + w2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + -4.5w + w2 = 0 + -2.5
-4.5w + w2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
-4.5w + w2 = -2.5

The w term is -4.5w.  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.
-4.5w + 5.0625 + w2 = -2.5 + 5.0625

Reorder the terms:
5.0625 + -4.5w + w2 = -2.5 + 5.0625

Combine like terms: -2.5 + 5.0625 = 2.5625
5.0625 + -4.5w + w2 = 2.5625

Factor a perfect square on the left side:
(w + -2.25)(w + -2.25) = 2.5625

Calculate the square root of the right side: 1.600781059

Break this problem into two subproblems by setting 
(w + -2.25) equal to 1.600781059 and -1.600781059.


Subproblem 1
w + -2.25 = 1.600781059

Simplifying
w + -2.25 = 1.600781059

Reorder the terms:
-2.25 + w = 1.600781059

Solving
-2.25 + w = 1.600781059

Solving for variable 'w'.

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

Add '2.25' to each side of the equation.
-2.25 + 2.25 + w = 1.600781059 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + w = 1.600781059 + 2.25
w = 1.600781059 + 2.25

Combine like terms: 1.600781059 + 2.25 = 3.850781059
w = 3.850781059

Simplifying
w = 3.850781059


Subproblem 2
w + -2.25 = -1.600781059

Simplifying
w + -2.25 = -1.600781059

Reorder the terms:
-2.25 + w = -1.600781059

Solving
-2.25 + w = -1.600781059

Solving for variable 'w'.

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

Add '2.25' to each side of the equation.
-2.25 + 2.25 + w = -1.600781059 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + w = -1.600781059 + 2.25
w = -1.600781059 + 2.25

Combine like terms: -1.600781059 + 2.25 = 0.649218941
w = 0.649218941

Simplifying
w = 0.649218941


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {3.850781059, 0.649218941}
Solution
w = {3.850781059, 0.649218941}

See similar equations:

| 3x-3y=16 | | A+3X=c | | 22=9+5x | | f(f-22)+72=0 | | 5-3(x-1)=2x+4 | | In(x+1)-In(x+2)=In(x) | | x=x^2+x+2 | | 13+2x=-10 | | x^2+2.5+2=0 | | x+(x+10000)+2(x+10000)=90000 | | -2x+6+4x=20 | | 15=10-2x | | 2y+6=40 | | 4r+30=16 | | x+(400-x)=160 | | 4x^2+16x+80=0 | | 2s+20=74-7s | | 4m-5.4=2m+3 | | 7x-6=5x+15-6x | | 6g+9=27 | | 10x=144-6x | | 4x^2-xy+y^2=25 | | (3-2x)+(4-3x)+(5-5x)=12+7x | | 8x+y=345 | | x^2+4x-110=0 | | 4x-8=7x+13 | | sin(x)=0.27 | | -5+5x-7x=-17 | | (4x+3)-(10x+11)=7+(13-4x) | | 4*4x=0 | | lg(x)3+lg(x)12=2 | | 4xsquare=0 |

Equations solver categories