Question
whats the complete square of the expression x2-12x-50
Answers
GPT-4o mini
To complete the square for the expression \(x^2 - 12x - 50\), follow these steps:
1. **Identify the coefficient of \(x\)**: The coefficient of \(x\) is \(-12\).
2. **Take half of the coefficient and square it**:
\[
\left(\frac{-12}{2}\right)^2 = (-6)^2 = 36
\]
3. **Add and subtract this square inside the expression**:
\[
x^2 - 12x + 36 - 36 - 50
\]
4. **Reorganize the terms**:
\[
(x^2 - 12x + 36) - 86
\]
5. **Form the complete square**:
\[
(x - 6)^2 - 86
\]
So, the expression \(x^2 - 12x - 50\) can be written as:
\[
(x - 6)^2 - 86
\]
1. **Identify the coefficient of \(x\)**: The coefficient of \(x\) is \(-12\).
2. **Take half of the coefficient and square it**:
\[
\left(\frac{-12}{2}\right)^2 = (-6)^2 = 36
\]
3. **Add and subtract this square inside the expression**:
\[
x^2 - 12x + 36 - 36 - 50
\]
4. **Reorganize the terms**:
\[
(x^2 - 12x + 36) - 86
\]
5. **Form the complete square**:
\[
(x - 6)^2 - 86
\]
So, the expression \(x^2 - 12x - 50\) can be written as:
\[
(x - 6)^2 - 86
\]