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

Transcript text: $\mathrm{x}^{2}-6 \mathrm{x}+1=0$ 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

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.

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

Step 1: Start with the given quadratic equation

The given quadratic equation is: \[ x^2 - 6x + 1 = 0 \]

Step 2: Move the constant term to the other side

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

Step 3: Complete the square

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

Step 4: Verify the equivalent form

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