Question

completing
complete the expression so it forms a perfect - square trinomial.
x² + 5x + ✓ 25/4
complete
x² + ▼ x + 49
do
14
7
7/2

Explanation:

Step1: Recall perfect - square trinomial formula

A perfect - square trinomial has the form \(a^{2}+2ab + b^{2}=(a + b)^{2}\) or \(a^{2}-2ab + b^{2}=(a - b)^{2}\). For the trinomial \(x^{2}+\square x + 49\), we know that \(a=x\) and \(b^{2}=49\), so \(b=\pm7\). But since the middle term is positive (we can assume the form is \((x + b)^{2}\) for simplicity here), and \(2ab=\square x\), with \(a = x\) and \(b = 7\), then \(2ab=2\times x\times7 = 14x\). So the coefficient of \(x\) should be 14.

Answer:

14