Let's solve the equation [tex]\( 5x^2 - 30x = 5 \)[/tex] by completing the square.
1. Rewrite the equation in standard form:
[tex]\( 5x^2 - 30x - 5 = 0 \)[/tex]
2. Divide the entire equation by 5, the coefficient of [tex]\( x^2 \)[/tex]:
[tex]\( x^2 - 6x - 1 = 0 \)[/tex]
3. Move the constant term to the right side of the equation:
[tex]\( x^2 - 6x = 1 \)[/tex]
4. Complete the square:
- Take half of the coefficient of [tex]\( x \)[/tex], which is [tex]\(-6\)[/tex], divide by 2, and square it:
[tex]\( \left( \frac{-6}{2} \right)^2 = 9 \)[/tex]
- Add and subtract this square inside the equation:
[tex]\( x^2 - 6x + 9 - 9 = 1 \)[/tex]
5. Rewrite the left side as a perfect square:
[tex]\( (x - 3)^2 - 9 = 1 \)[/tex]
6. Move the [tex]\(-9\)[/tex] to the right side:
[tex]\( (x - 3)^2 = 1 + 9 \)[/tex]
7. Simplify the right side:
[tex]\( (x - 3)^2 = 10 \)[/tex]
Thus, the correct answer is:
A. [tex]\((x - 3)^2 = 10\)[/tex]
