To solve the polynomial equation [tex]\(x^2 - 4x + 1 = 0\)[/tex] by completing the square, let's go through the steps Fiona should follow in detail.
1. Ensure the coefficient of [tex]\(x^2\)[/tex] is 1: In this case, the coefficient is already 1, so no adjustments are necessary.
2. Move the constant term to the opposite side of the equation:
Subtract the constant term [tex]\(1\)[/tex] from both sides to isolate the [tex]\(x\)[/tex] terms. This step is crucial for completing the square. The equation then becomes:
[tex]\[
x^2 - 4x + 1 - 1 = 0 - 1
\][/tex]
Simplifying this, we get:
[tex]\[
x^2 - 4x = -1
\][/tex]
Therefore, Fiona's first step should be "isolating the constant 1".
If we look at the provided options:
1. isolating the constant [tex]\(1\)[/tex]
2. adding [tex]\(4\)[/tex] to both sides of the equation
3. isolating the second term, [tex]\(-4x\)[/tex]
4. adding [tex]\(1\)[/tex] to both sides of the equation
The correct first step is isolating the constant 1.
