Perfect square

Perfect square quadratics are of the form

$(x + a)(x + a) = x^2 + 2a + a^2$

$2a = 12 \Longrightarrow a = 6$

$a^2 = 6^2 \Longrightarrow \boxed{m = 36}$

12X = 6X + 6X
mX^2 = (6X)(6X)
m = 36X^2
m = 36

Solution 1.

For the quadratic expression $Ax^2 + Bx + C$ to be perfect square, $B^2 = 4AC$ .

$B^2 = 4AC$ $\implies$ $12^2 = 4(1)(m)$ $\implies$ $m = \frac{144}{4} = 36$

Solution 2.

By completing the square,

step 1. Divide the coefficient of $x$ by $2$ .

step 2. Square the result in step 1. This is now the value to be added to $Ax^2 + Bx$ to make it a perfect square.

By applying the steps above,

step 1. $\frac{12}{2} = 6$

step 2. $6^2 = 36$

Therefore, $m = 36$ .