Question

when rewriting $x^2 - 4x + 4 = 49$ into perfect square form, what goes into the blank $(x \dots )^2 = 49$

Explanation:

Step1: Recall perfect square formula

The perfect square trinomial formula is \((x - a)^2 = x^2 - 2ax + a^2\).

Step2: Compare with given trinomial

Given trinomial is \(x^2 - 4x + 4\). Comparing with \(x^2 - 2ax + a^2\), we have \(-2a=-4\), so \(a = 2\). Thus, \(x^2 - 4x + 4=(x - 2)^2\).

Answer:

\(-2\)