# Fiona is completing the square to solve the polynomial equation x^{2} - 4x + 1 = 0. What should be her first step?

Isolating the constant 1

Adding 4 to both sides of the equation

Isolating the second term, 4x

Adding 1 to both sides of the equation

**Solution:**

The given polynomial equation is

x^{2} - 4x + 1 = 0

Let us isolate 1

x^{2} - 4x = 1

We know that

2ab = -4x

2xb = -4x

b = -2

Let us take the square of b and add it to both sides

x^{2} - 4x + (-2)^{2} = 1 + (-2)^{2}

x^{2} - 4x + 4 = 1 + 4

x^{2} - 4x + 4 = 5

(x - 2)^{2} = 5

Taking square root on both sides

√(x - 2)^{2} = √5

(x - 2) = ±√5

x = ±√5 + 2

Therefore, the first step should be isolating the constant 1.

## Fiona is completing the square to solve the polynomial equation x^{2} - 4x + 1 = 0. What should be her first step?

**Summary:**

Fiona is completing the square to solve the polynomial equation x^{2} - 4x + 1 = 0. Her first step should be isolating the constant 1.

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