3w^2-6w+2=0

Simple and best practice solution for 3w^2-6w+2=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 3w^2-6w+2=0 equation:


Simplifying
3w2 + -6w + 2 = 0

Reorder the terms:
2 + -6w + 3w2 = 0

Solving
2 + -6w + 3w2 = 0

Solving for variable 'w'.

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

Divide each side by '3'.
0.6666666667 + -2w + w2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + -2w + -0.6666666667 + w2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + -2w + w2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + -2w + w2 = 0 + -0.6666666667
-2w + w2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
-2w + w2 = -0.6666666667

The w term is -2w.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2w + 1 + w2 = -0.6666666667 + 1

Reorder the terms:
1 + -2w + w2 = -0.6666666667 + 1

Combine like terms: -0.6666666667 + 1 = 0.3333333333
1 + -2w + w2 = 0.3333333333

Factor a perfect square on the left side:
(w + -1)(w + -1) = 0.3333333333

Calculate the square root of the right side: 0.577350269

Break this problem into two subproblems by setting 
(w + -1) equal to 0.577350269 and -0.577350269.

Subproblem 1

w + -1 = 0.577350269 Simplifying w + -1 = 0.577350269 Reorder the terms: -1 + w = 0.577350269 Solving -1 + w = 0.577350269 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + w = 0.577350269 + 1 Combine like terms: -1 + 1 = 0 0 + w = 0.577350269 + 1 w = 0.577350269 + 1 Combine like terms: 0.577350269 + 1 = 1.577350269 w = 1.577350269 Simplifying w = 1.577350269

Subproblem 2

w + -1 = -0.577350269 Simplifying w + -1 = -0.577350269 Reorder the terms: -1 + w = -0.577350269 Solving -1 + w = -0.577350269 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + w = -0.577350269 + 1 Combine like terms: -1 + 1 = 0 0 + w = -0.577350269 + 1 w = -0.577350269 + 1 Combine like terms: -0.577350269 + 1 = 0.422649731 w = 0.422649731 Simplifying w = 0.422649731

Solution

The solution to the problem is based on the solutions from the subproblems. w = {1.577350269, 0.422649731}

See similar equations:

| 5/9(f-32)=-62.5 | | 22/206=?/100 | | X=-4.8+-1.6y | | y/4-5=1 | | bn=4n-2 | | -6w=36 | | 4*5-3*2-5= | | x+9-5x=27 | | Y^0x/y^7 | | 28-3x=5x+5 | | 5u-3=-7(u-3) | | x-0.23x=473.17 | | g+5h= | | 2x-8=x-16 | | 2x+10+4x-17=59 | | -277=5(1+8x)+7x | | 8(k+11)+7=3k-12 | | 394.06=180+0.77x | | 20x+8=x | | Y+18=-6 | | 8w-15=25 | | x+2=x-16 | | 79/-9 | | -5+2=30 | | (3/5)y-(1/3)=-(3/2) | | X-4=16/2 | | 55x+500=35 | | 7y+8y-8= | | F(2)+1=3(2)+2 | | Dx-49-1=0 | | N/5=.6 | | 6p-2-3p=26 |

Equations solver categories