Algebra

x^2 - 4x + 4 = 0

Step-by-step solution with explanation

Final Answer

(a double root — one unique solution)

Step-by-step solution

1

Recognize a perfect square trinomial

Notice the pattern: the first term is a perfect square, the last term is a perfect square, and the middle term is twice the product of their square roots. This tells us it factors into a perfect square.
2

Factor the left side completely

We rewrite the trinomial as a binomial squared. Check: ✓. This is called a perfect square trinomial.
3

Take the square root of both sides

To undo the square, we take the square root of both sides. The square root of 0 is just 0.
4

Solve for x

Add 2 to both sides to isolate x. Because both factors are identical, there is only one unique solution — called a repeated root or double root.

Understanding this problem

Learning Insight

A perfect square trinomial always has a double root — meaning the parabola just touches the x-axis at one point instead of crossing it. This happens because both factors are the same, so the equation only has one unique answer even though technically it counts as two roots.

Quick Tip

Spot a perfect square trinomial fast: check if the last term equals half the middle coefficient squared. Here, half of 4 is 2, and ✓. If it matches, it factors as .

Common Mistake

Students often write two different answers like and , confusing this with a difference of squares. Remember: gives only , not .