Solve the equation by finding the square root.

4u2 + 4u + 1 = 75

I will assume you mean

4u^2 + 4u + 1 = 75
(2u+1)^2 = 75
2u + 1 = ± √75
2u = -1 ± 5√3
u = (-1 ± 5√3)/2

Find the square root of 4u2- 8u.

To solve this equation by finding the square root, we first need to isolate the squared term by moving the constants to the other side of the equation.

Start by subtracting 1 from both sides:

4u^2 + 4u = 74

Now, let's divide the entire equation by 4 to simplify it:

u^2 + u = 74/4

This simplifies to:

u^2 + u = 18.5

Next, we want to complete the square by adding a value to both sides of the equation to make the left side a perfect square trinomial.

Take half of the coefficient of the linear term (which is 1) and square it:

(1/2)^2 = 1/4

Add 1/4 to both sides of the equation:

u^2 + u + 1/4 = 18.5 + 1/4

This gives us a perfect square trinomial on the left side of the equation:

(u + 1/2)^2 = 18.75

Now, we can take the square root of both sides to solve for u:

u + 1/2 = ±√18.75

Subtract 1/2 from both sides:

u = -1/2 ± √18.75

Therefore, the solutions to the equation are:

u = -1/2 + √18.75

u = -1/2 - √18.75