Question
Complete the square x^2-12x
Answers
GPT-4o mini
To complete the square for the expression \( x^2 - 12x \), follow these steps:
1. **Take the coefficient of \( x \)**, which is \(-12\).
2. **Divide it by 2**:
\[
\frac{-12}{2} = -6
\]
3. **Square the result**:
\[
(-6)^2 = 36
\]
Now, rewrite the expression by adding and subtracting this square inside the equation:
\[
x^2 - 12x = (x^2 - 12x + 36) - 36
\]
This allows us to express it as a perfect square:
\[
= (x - 6)^2 - 36
\]
So the completed square form of \( x^2 - 12x \) is:
\[
(x - 6)^2 - 36
\]
1. **Take the coefficient of \( x \)**, which is \(-12\).
2. **Divide it by 2**:
\[
\frac{-12}{2} = -6
\]
3. **Square the result**:
\[
(-6)^2 = 36
\]
Now, rewrite the expression by adding and subtracting this square inside the equation:
\[
x^2 - 12x = (x^2 - 12x + 36) - 36
\]
This allows us to express it as a perfect square:
\[
= (x - 6)^2 - 36
\]
So the completed square form of \( x^2 - 12x \) is:
\[
(x - 6)^2 - 36
\]