Of course! Let's complete each statement for solving [tex]\( x^2 - 4x + 3 = 0 \)[/tex] using the process of completing the square step by step.
1. Isolate the constant by subtracting 3 from both sides of the equation.
[tex]\[
x^2 - 4x + 3 - 3 = 0 - 3 \implies x^2 - 4x = -3
\][/tex]
2. Add 4 to both sides of [tex]\( x^2 - 4x = -3 \)[/tex] to form a perfect square trinomial while keeping the equation balanced.
[tex]\[
x^2 - 4x + 4 = -3 + 4 \implies x^2 - 4x + 4 = 1
\][/tex]
3. Write the trinomial [tex]\( x^2 - 4x + 4 \)[/tex] as [tex]\( (x-2) \)[/tex] squared.
[tex]\[
x^2 - 4x + 4 = (x - 2)^2
\][/tex]
4. Use the square root property of equality to get [tex]\( x-2 = \pm \)[/tex] 1 [tex]\(\checkmark\)[/tex].
[tex]\[
(x - 2)^2 = 1 \implies x - 2 = \pm 1
\][/tex]
5. Isolate the variable to get solutions of 1 and 3.
[tex]\[
\text{If } x - 2 = 1, \text{ then } x = 2 + 1 = 3
\][/tex]
[tex]\[
\text{If } x - 2 = -1, \text{ then } x = 2 - 1 = 1
\][/tex]
Thus, the solutions to the equation [tex]\( x^2 - 4x + 3 = 0 \)[/tex] are [tex]\( x = 3 \)[/tex] and [tex]\( x = 1 \)[/tex].
