Answer:
(2x + 1)^2 = 7
Explanation:
To write the quadratic equation 4x^2 + 8x - 10 = 0 in vertex form, we need to first complete the square. To do this, we need to add and subtract the same value to the quadratic term and the linear term so that the resulting quadratic has the form (x - h)^2 = k.
In this case, we need to add and subtract the square of half of the coefficient of the linear term, which is 8/2 = 4. This gives us the equation:
4x^2 + 8x + 4 - 4 - 10 = 0
This simplifies to 4(x^2 + 2x + 1) - 14 = 0, which can be rewritten as (2x + 1)^2 - 7 = 0.
To put this in vertex form, we need to rewrite the right side of the equation as a perfect square, so we add 7 to both sides to get (2x + 1)^2 = 7.
Then, we take the square root of both sides to get 2x + 1 = ±√7. We can then solve for x to get x = -1/2 ± √7/2.
Therefore, the equation 4x^2 + 8x - 10 = 0 can be written in vertex form as (2x + 1)^2 = 7.