Question

Complete each statement in the steps to solve x2 – 4x + 3 = 0 using the process of completing the square.

Isolate the constant by
both sides of the equation.
Add
to both sides of x2 – 4x = –3 to form a perfect square trinomial while keeping the equation balanced.
Write the trinomial x2 – 4x + 4 as
squared.
Use the square root property of equality to get x – 2 = ±
.
Isolate the variable to get solutions of 1 and 3.

Answer 1

Explanation:

x^2 – 4x + 3 = 0

To solve by completing the square:

1. Isolate the constant by adding the negative of the constant (-3) to both sides of the equation.

x^2 -4x+3-3 = 0-3

x^2 – 4x = -3

2. Add 4 to both sides of x2 – 4x = –3 to form a perfect square trinomial while keeping the equation balanced.

x^2 – 4x +4 = -3+4

x^2 – 4x +4 = 1

3. Write the trinomial x^2 – 4x + 4 as (x-2) (x-2) = (x-2) squared.

(x-2)^2 = 1

4. Use the square root property of equality to get x – 2 = ±1

Taking the square root of each side

sqrt((x-2)^2) = ±1

x-2 = ±1

5. Isolate the variable to get solutions of 1 and 3.

x-2 = 1 x-2 = -1

x=1+2 x=2-1

x=3 x=1