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