(2w-1)^2=4(w-3)^2
Expand both sides of the equation, then simplify:
4w^1 - 4w + 1 = 4w^2 - 24w + 36
......
.....
w = 7/4
To solve the equation (2w-1)^2 = 4(w-3)^2, we need to expand both sides of the equation and then simplify.
First, let's expand the left side of the equation:
(2w - 1)^2 = (2w - 1)(2w - 1)
= (2w) * (2w) + (2w) * (-1) + (-1) * (2w) + (-1) * (-1)
= 4w^2 - 2w - 2w + 1
= 4w^2 - 4w + 1
Now let's expand the right side of the equation:
4(w - 3)^2 = 4(w - 3)(w - 3)
= 4(w * w - 3w - 3w + 9)
= 4(w^2 - 6w + 9)
= 4w^2 - 24w + 36
So now we have the expanded equation:
4w^2 - 4w + 1 = 4w^2 - 24w + 36
Next, we can simplify the equation by combining like terms:
4w^2 - 4w + 1 - 4w^2 + 24w - 36 = 0
-8w + 1 - 36 = 0
-8w - 35 = 0
To isolate w, we can move -35 to the other side of the equation:
-8w = 35
w = 35 / -8
w = -35/8
w = -4.375
So the value of w that satisfies the equation is w = -4.375.