Question

Rewrite the function by completing the square f(x)=x^2+x-30

Answer 1

Rewritten the function by completing the square, will get f(x) = (x + 1/2)^2 - 121/4.

Step-by-step explanation:

To rewrite the function by completing the square, we need to follow the steps below:

1. Move the constant term to the other side of the equation:
2. x^2 + x = 30
3. Take half of the coefficient of x and square it:
4. (1/2)^2 = 1/4
5. Add this value to both sides of the equation:
6. x^2 + x + 1/4 = 30 + 1/4
7. Factor the perfect square trinomial on the left side:
8. (x + 1/2)^2 = 30 + 1/4
9. Simplify the right side of the equation:
10. (x + 1/2)^2 = 121/4
11. Take the square root of both sides:
12. x + 1/2 = ±√(121/4)
13. Solve for x:
14. x = -1/2 ±√(121/4)

Therefore, the rewritten function is f(x) = (x + 1/2)^2 - 121/4.