Answer:
To turn -5/7 and 8 into a quadratic equation, we first need to convert 8 into an equation by adding 8 to both sides. The equation becomes: -5/7 = x^2 + 8. Then, we can expand the right side into a complete square, using the formula (b/2)^2. The equation becomes:
-5/7 = (x^2 + 8) + (4/2)^2
-5/7 = x^2 + 8 + 4
-5/7 = x^2 + 12
Finally, we can rearrange the equation to make the right side equal to 0, and then factor it. The final equation is:
x^2 + 12 + 5/7 = 0
x^2 + 12 + 5/7 = (x + 6/√7)(x + 6/√7) = 0
Explanation:
In the first step, we added 8 to both sides to make the equation -5/7 = x^2 + 8. In the next step, we added 4 to the right side to complete the square. The purpose of completing the square is to get a perfect square on the right side, which will make it easier to factor the equation.
Next, we rearranged the equation to make the right side equal to 0, so that we can factor the equation. The equation x^2 + 12 + 5/7 = 0 can be factored as (x + 6/√7)(x + 6/√7) = 0, where (x + 6/√7) is a binomial that satisfies the equation.