Question

Rewrite the equation 0=4x��+4x-10 in the form (x-p)��=q.

Answer 1

To rewrite the equation in the form (x-p)²=q, complete the square to get the final equation: (x+½)²=⅚.

Step-by-step explanation:

To rewrite the equation 0=4x²+4x-10 in the form (x-p)²=q, we first need to complete the square. The process of completing the square involves creating a perfect square trinomial from the quadratic equation, which allows us to express the equation in the desired form.

First, we need to isolate the x terms by factoring out the coefficient of the x² term from the x terms:

1. Divide the equation by 4 to simplify: 0=(x²+x-⅓).
2. Move the constant term to the other side: x²+x=⅓.
3. Add and subtract the square of half the coefficient of x inside the equation: x²+x+¼-¼=⅓.
4. Rewrite the equation grouping the perfect square trinomial: (x+½)²-¼=⅓.
5. Combine the constants on the right-hand side: (x+½)²=⅓+¼.
6. Simplify the constant term: (x+½)²=⅚.

So, the equation in the form (x-p)²=q is (x+½)²=⅚.