2w(4w+1)=1
If you question is how to factor it, you aready did.
If the question is the value of w, it is best to rewrite in standard polynomial equation form first.
8w^2 + 2x -1 = 0
(4x -1)(2x +1) = 0
x = 1/4 or -1/2
thank you yes i was trying to figure out how to solve for w
To solve the equation 2w(4w+1) = 1, we can follow these steps:
1. Distribute 2w across the terms inside the parentheses:
2w * 4w + 2w * 1 = 1.
This simplifies to: 8w^2 + 2w = 1.
2. Move all the terms to one side of the equation to set it equal to zero. Let's subtract 1 from both sides:
8w^2 + 2w - 1 = 0.
3. Now, we have a quadratic equation in the form of ax^2 + bx + c = 0. In this case, our equation is 8w^2 + 2w - 1 = 0, which means:
a = 8
b = 2
c = -1.
4. To solve this quadratic equation, we can use the quadratic formula:
w = (-b ± sqrt(b^2 - 4ac)) / 2a.
Substituting the values, we have:
w = (-2 ± sqrt(2^2 - 4*8*(-1))) / (2*8).
5. Simplifying this equation further, we get:
w = (-2 ± sqrt(4 + 32)) / 16,
w = (-2 ± sqrt(36)) / 16.
6. Taking the square root of 36 gives us two possible values for w:
w = (-2 + 6) / 16 or w = (-2 - 6) / 16.
7. Simplifying further, we have:
w = 4 / 16 or w = -8 / 16.
8. Finally, simplifying the fractions, we get the solutions:
w = 1/4 or w = -1/2.
Therefore, the solutions to the equation 2w(4w+1) = 1 are w = 1/4 or w = -1/2.