Question
Which equation is equivalent to x^2 - 6x + 4 = 0? Hint: After you complete the square, move constant to right side to rewrite in the form (x - p)2 = q and constant term sign will change.
A.
(x-3)² = 5
B.
(x-3)² = -4
C.
(x-3)² = 6
D.
(x-3)² = 9
A.
(x-3)² = 5
B.
(x-3)² = -4
C.
(x-3)² = 6
D.
(x-3)² = 9
Answers
GPT-4o mini
To rewrite the equation \(x^2 - 6x + 4 = 0\) in the form \((x - p)^2 = q\) by completing the square, follow these steps:
1. **Start with the original equation**:
\[
x^2 - 6x + 4 = 0
\]
2. **Move the constant term to the right side**:
\[
x^2 - 6x = -4
\]
3. **Complete the square**:
- Take half of the coefficient of \(x\) (which is \(-6\)), square it, and add it to both sides.
- Half of \(-6\) is \(-3\), and squaring it gives \((-3)^2 = 9\).
4. **Add 9 to both sides**:
\[
x^2 - 6x + 9 = -4 + 9
\]
5. **Rewrite the left-hand side as a perfect square**:
\[
(x - 3)^2 = 5
\]
Thus, the equation \(x^2 - 6x + 4 = 0\) can be rewritten as:
\[
(x - 3)^2 = 5
\]
So the correct answer is **A**: \((x - 3)^2 = 5\).
1. **Start with the original equation**:
\[
x^2 - 6x + 4 = 0
\]
2. **Move the constant term to the right side**:
\[
x^2 - 6x = -4
\]
3. **Complete the square**:
- Take half of the coefficient of \(x\) (which is \(-6\)), square it, and add it to both sides.
- Half of \(-6\) is \(-3\), and squaring it gives \((-3)^2 = 9\).
4. **Add 9 to both sides**:
\[
x^2 - 6x + 9 = -4 + 9
\]
5. **Rewrite the left-hand side as a perfect square**:
\[
(x - 3)^2 = 5
\]
Thus, the equation \(x^2 - 6x + 4 = 0\) can be rewritten as:
\[
(x - 3)^2 = 5
\]
So the correct answer is **A**: \((x - 3)^2 = 5\).