2w^2+w=12

Simple and best practice solution for 2w^2+w=12 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^2+w=12 equation:


Simplifying
2w2 + w = 12

Reorder the terms:
w + 2w2 = 12

Solving
w + 2w2 = 12

Solving for variable 'w'.

Reorder the terms:
-12 + w + 2w2 = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + w + 2w2 = 0

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

Divide each side by '2'.
-6 + 0.5w + w2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 0.5w + 6 + w2 = 0 + 6

Reorder the terms:
-6 + 6 + 0.5w + w2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 0.5w + w2 = 0 + 6
0.5w + w2 = 0 + 6

Combine like terms: 0 + 6 = 6
0.5w + w2 = 6

The w term is w.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.5w + 0.25 + w2 = 6 + 0.25

Reorder the terms:
0.25 + 0.5w + w2 = 6 + 0.25

Combine like terms: 6 + 0.25 = 6.25
0.25 + 0.5w + w2 = 6.25

Factor a perfect square on the left side:
(w + 0.5)(w + 0.5) = 6.25

Calculate the square root of the right side: 2.5

Break this problem into two subproblems by setting 
(w + 0.5) equal to 2.5 and -2.5.

Subproblem 1

w + 0.5 = 2.5 Simplifying w + 0.5 = 2.5 Reorder the terms: 0.5 + w = 2.5 Solving 0.5 + w = 2.5 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + w = 2.5 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = 2.5 + -0.5 w = 2.5 + -0.5 Combine like terms: 2.5 + -0.5 = 2 w = 2 Simplifying w = 2

Subproblem 2

w + 0.5 = -2.5 Simplifying w + 0.5 = -2.5 Reorder the terms: 0.5 + w = -2.5 Solving 0.5 + w = -2.5 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + w = -2.5 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = -2.5 + -0.5 w = -2.5 + -0.5 Combine like terms: -2.5 + -0.5 = -3 w = -3 Simplifying w = -3

Solution

The solution to the problem is based on the solutions from the subproblems. w = {2, -3}

See similar equations:

| c^2+7cd-18d^2=0 | | w=48+(4/7)w | | 10-2q=1.5q+1 | | =(x+9)(9x+1) | | 3.2x=22.2 | | 6x+y^2=42 | | f(x)=50/x^2-25 | | 3x^2y+27xy-87y=0 | | 4[X+7]=80 | | 12x12x5y4z2/18x^1y^7z^2 | | 1=3/2Q+1 | | 1=10-2Q | | -13y+11x=3 | | x(2-x)=15 | | -13+11x=3 | | P=10+2 | | cos^2x-sin^2x=-1/5 | | =10+2Q | | f(x)=-x^3+9x | | (-2)+3j=4 | | 6-3x=4(8-x) | | 3(x+1)=2x+2+x+1 | | 5=(y/4)-(2y) | | 2x^2-5x+2y^2-3y=0 | | 3y+5=(-16) | | 8.7y=3.9y+9.6 | | 9log(2x-1)=3 | | 10*t=9.7637 | | 6k^2+1-6k=0 | | 9y-12=-32+4y | | 2=x-3x+4 | | F(x)=8x^2-40x+50 |

Equations solver categories