3w^2-2w=27

Simple and best practice solution for 3w^2-2w=27 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^2-2w=27 equation:


Simplifying
3w2 + -2w = 27

Reorder the terms:
-2w + 3w2 = 27

Solving
-2w + 3w2 = 27

Solving for variable 'w'.

Reorder the terms:
-27 + -2w + 3w2 = 27 + -27

Combine like terms: 27 + -27 = 0
-27 + -2w + 3w2 = 0

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

Divide each side by '3'.
-9 + -0.6666666667w + w2 = 0

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + -0.6666666667w + 9 + w2 = 0 + 9

Reorder the terms:
-9 + 9 + -0.6666666667w + w2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -0.6666666667w + w2 = 0 + 9
-0.6666666667w + w2 = 0 + 9

Combine like terms: 0 + 9 = 9
-0.6666666667w + w2 = 9

The w term is -0.6666666667w.  Take half its coefficient (-0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
-0.6666666667w + 0.1111111112 + w2 = 9 + 0.1111111112

Reorder the terms:
0.1111111112 + -0.6666666667w + w2 = 9 + 0.1111111112

Combine like terms: 9 + 0.1111111112 = 9.1111111112
0.1111111112 + -0.6666666667w + w2 = 9.1111111112

Factor a perfect square on the left side:
(w + -0.3333333334)(w + -0.3333333334) = 9.1111111112

Calculate the square root of the right side: 3.018461713

Break this problem into two subproblems by setting 
(w + -0.3333333334) equal to 3.018461713 and -3.018461713.

Subproblem 1

w + -0.3333333334 = 3.018461713 Simplifying w + -0.3333333334 = 3.018461713 Reorder the terms: -0.3333333334 + w = 3.018461713 Solving -0.3333333334 + w = 3.018461713 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + w = 3.018461713 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + w = 3.018461713 + 0.3333333334 w = 3.018461713 + 0.3333333334 Combine like terms: 3.018461713 + 0.3333333334 = 3.3517950464 w = 3.3517950464 Simplifying w = 3.3517950464

Subproblem 2

w + -0.3333333334 = -3.018461713 Simplifying w + -0.3333333334 = -3.018461713 Reorder the terms: -0.3333333334 + w = -3.018461713 Solving -0.3333333334 + w = -3.018461713 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + w = -3.018461713 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + w = -3.018461713 + 0.3333333334 w = -3.018461713 + 0.3333333334 Combine like terms: -3.018461713 + 0.3333333334 = -2.6851283796 w = -2.6851283796 Simplifying w = -2.6851283796

Solution

The solution to the problem is based on the solutions from the subproblems. w = {3.3517950464, -2.6851283796}

See similar equations:

| 4(5x-6)-4(2x+1)=0 | | 4z+4x-6z-x= | | 0.15x^2-3.15X+2=0 | | 9n-6=-51 | | 8z+4=20 | | 3z+-3=9 | | -3x+4y-2x= | | 166-5x=41 | | -3z-(-9z)= | | 4(6-2x)-3(3-4x)=0 | | 18+2x=8x-13 | | 9x-3x+x=42 | | 5x-8=50+2x | | 1+3x=5-6x | | 16=3h-4 | | 11w^2-14w+3=0 | | 3n+-7=2n+5 | | q*3+10=-3 | | 7-5x=4x-12 | | 8(5+3x)=208 | | 18=y-10y | | 12x-(3-x)+2x=41-(-1) | | 5x+2y+4x+8y= | | 0=-6+6x-2y | | x^4-6x^3-135x^2-864x+1296=0 | | X^2=2x+30 | | 4/7-1/14= | | 5u+8=18 | | 4/7-1/14=1 | | 6(5)=u | | 5u+8=15 | | 8=y-10y |

Equations solver categories