Questions: x^2-6x+1=0 is a quadratic equation in x. Which of the following is the corresponding equivalent form (x-p)^2=q? (x-3)^2=10 (x-6)^2=8 (x-6)^2=10 (x-3)^2=8

Solution Steps

To convert the given quadratic equation $x^2 - 6x + 1 = 0$ into the form $(x - p)^2 = q$, we need to complete the square.

1. Start with the quadratic equation $x^2 - 6x + 1 = 0$.
2. Move the constant term to the other side: $x^2 - 6x = -1$.
3. Add and subtract the square of half the coefficient of $x$ (which is $-6/2 = -3$) inside the equation: $x^2 - 6x + 9 = -1 + 9$.
4. Simplify the equation to get it in the form $(x - p)^2 = q$.

The given quadratic equation is: $$x^2 - 6x + 1 = 0$$

Rearrange the equation by moving the constant term to the right side: $$x^2 - 6x = -1$$

To complete the square, add and subtract the square of half the coefficient of $x$ (which is $-6/2 = -3$): $$x^2 - 6x + 9 = -1 + 9$$ $$(x - 3)^2 = 8$$

The equivalent form of the given quadratic equation is: $$(x - 3)^2 = 8$$

Final Answer