Question

Solve the equation by completing the square. question 4w(w−3)=24

Answer 1

The solution to the equation 4w(w−3)=24 by completing the square is w = 3 ± 2.

Step-by-step explanation:

Completing the square involves transforming a quadratic equation into a perfect square trinomial. In this case, the given equation is 4w(w−3)=24. To complete the square, we first divide both sides by 4 to simplify the equation to w(w−3) = 6. Next, we add
`(-3)/(2) ^(2) =(9)/(4)` to both sides to create a perfect square trinomial on the left side. This results in the equation
`(w-3)/(2)^(2) =(33)/(4)`.

Taking the square root of both sides and solving for w, we get two solutions: w =
`(3)/(2) +√(33/2)` and
`w = 3/2 - √(33/2)`. These can be further simplified to w = 3 + 2 and w = 3 - 2, which are the final solutions.

In summary, the solution to the equation 4w(w−3)=24 by completing the square is w = 3 ± 2, where the ± represents the two possible solutions. This method allows us to find the values of w that satisfy the given equation and complete the square to facilitate the solution process.