What is the intermediate step in the form $$ (x+a)^{2}=b $$ as a result of completing the square for the following equation? $$ 4 x^{2}-72 x=-68 $$

Question

UpStudy AI · Accepted Answer

To complete the square for the equation

$$
4x^{2} - 72x = -68,
$$

follow these steps:

1. **Divide by 4** to make the coefficient of $$x^2$$ equal to 1:

$$
   x^{2} - 18x = -17.
   $$

2. **Complete the square** on the left side. Take half of the coefficient of $$x$$ (which is $$-18$$), square it, and add it to both sides:

$$
   x^{2} - 18x + \left(\frac{-18}{2}\right)^2 = -17 + \left(\frac{-18}{2}\right)^2.
   $$
   
   $$
   x^{2} - 18x + 81 = 64.
   $$

3. **Rewrite the left side** as a perfect square:

$$
   (x - 9)^2 = 64.
   $$

The **intermediate step** in the form $$ (x + a)^2 = b $$ is:

$$
(x - 9)^2 = 64.
$$

**Answer:** After completing the square, an intermediate step is ( x – 9 ) squared equals 64, that is

(x−9)² = 64
After completing the square, an intermediate step is $$ (x - 9)^2 = 64 $$.

What is the intermediate step in the form \( (x+a)^{2}=b \) as a result of completing the square for the following equation? \[ 4 x^{2}-72 x=-68 \]