Question

question 10 (mandatory) (1 point) saved
what number must you add to $x^2 + 12x$ to create a perfect square?
\bigcirc a) 6
\bigcirc b) 36
\bigcirc c) 144
\bigcirc d) 12

Explanation:

Step1: Recall perfect square formula

A perfect square trinomial is of the form \(x^2 + 2bx + b^2=(x + b)^2\). For the expression \(x^2+12x\), compare with \(x^2 + 2bx\), we have \(2b = 12\).

Step2: Solve for b

From \(2b=12\), divide both sides by 2: \(b=\frac{12}{2}=6\).

Step3: Find the constant term

The constant term to add is \(b^2\). Substitute \(b = 6\), we get \(b^2=6^2 = 36\). So we add 36 to \(x^2 + 12x\) to get \((x + 6)^2=x^2+12x + 36\).

Answer:

b) 36