w(2w+3)=3

Simple and best practice solution for w(2w+3)=3 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 w(2w+3)=3 equation:


Simplifying
w(2w + 3) = 3

Reorder the terms:
w(3 + 2w) = 3
(3 * w + 2w * w) = 3
(3w + 2w2) = 3

Solving
3w + 2w2 = 3

Solving for variable 'w'.

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

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

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

Divide each side by '2'.
-1.5 + 1.5w + w2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + 1.5w + 1.5 + w2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + 1.5w + w2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + 1.5w + w2 = 0 + 1.5
1.5w + w2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
1.5w + w2 = 1.5

The w term is 1.5w.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5w + 0.5625 + w2 = 1.5 + 0.5625

Reorder the terms:
0.5625 + 1.5w + w2 = 1.5 + 0.5625

Combine like terms: 1.5 + 0.5625 = 2.0625
0.5625 + 1.5w + w2 = 2.0625

Factor a perfect square on the left side:
(w + 0.75)(w + 0.75) = 2.0625

Calculate the square root of the right side: 1.436140662

Break this problem into two subproblems by setting 
(w + 0.75) equal to 1.436140662 and -1.436140662.

Subproblem 1

w + 0.75 = 1.436140662 Simplifying w + 0.75 = 1.436140662 Reorder the terms: 0.75 + w = 1.436140662 Solving 0.75 + w = 1.436140662 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + w = 1.436140662 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + w = 1.436140662 + -0.75 w = 1.436140662 + -0.75 Combine like terms: 1.436140662 + -0.75 = 0.686140662 w = 0.686140662 Simplifying w = 0.686140662

Subproblem 2

w + 0.75 = -1.436140662 Simplifying w + 0.75 = -1.436140662 Reorder the terms: 0.75 + w = -1.436140662 Solving 0.75 + w = -1.436140662 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + w = -1.436140662 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + w = -1.436140662 + -0.75 w = -1.436140662 + -0.75 Combine like terms: -1.436140662 + -0.75 = -2.186140662 w = -2.186140662 Simplifying w = -2.186140662

Solution

The solution to the problem is based on the solutions from the subproblems. w = {0.686140662, -2.186140662}

See similar equations:

| 10m^5=85 | | 20-2(2x-7)=3(4x+10) | | 7y(y+7)= | | 4x^2-9=x | | -4x^2-68x-280=0 | | 0.0075x^2-14x+1200=0 | | -5x^2+65x-150=0 | | 12m+9=25m+35 | | 1/x=4/3x-1 | | 6e^10/3e^2 | | -10x^2+90x+360=0 | | 6z^2-11z+3=0 | | x^2+85=0 | | X=99-98 | | 1/2x-8=1 | | 0.01125x^2-13.05x+1800=0 | | 0.0075x^2+2x+1200=0 | | 12.6/7=9/5 | | m/7=9/5 | | X-3=0.5x+2 | | -3(7x-51)-8(3+7x)=-36+78x | | X^3-2x^2-10=0 | | (2x+7)+(-10x-4)=3(-x+12) | | 178=-r-4(-1+7r) | | 6(8-5/6x) | | y=8x+6b | | x+35+x-23=180 | | 50+6*x= | | 8k+15=-17 | | 10d-22=-2 | | 15g^2=0 | | 13x+10=16x |

Equations solver categories