Fiona is completing the square to solve the polynomial equation x² - 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

x² - 4x + 1 = 0

Let us isolate 1

x² - 4x = 1

We know that

2ab = -4x

2xb = -4x

b = -2

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

x² - 4x + (-2)² = 1 + (-2)²

x² - 4x + 4 = 1 + 4

x² - 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.

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Fiona is completing the square to solve the polynomial equation x² - 4x + 1 = 0. What should be her first step?

Summary:

Fiona is completing the square to solve the polynomial equation x² - 4x + 1 = 0. Her first step should be isolating the constant 1.