Question

Solve 3x2 + 12x = 3.

Answer 1

Answer:  The correct option is (D) $x=-2\pm\sqrt5.$

Step-by-step explanation:  We are given to solve the following quadratic equation :

$3x^2+12x=3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

We will be using the method of COMPLETING THE SQUARE to solve the given problem where the following square formula is used :

$a^2+2ab+b^2=(a+b)^2.$

From equation (i), we have

$3x^2+12x=3\\\\\Rightarrow 3(x^2+4x)=3\\\\\Rightarrow x^2+4x=1\\\\\Rightarrow x^2+2\times x\times2+2^2=1+2^2\\\\\Rightarrow (x+2)^2=1+4\\\\\Rightarrow (x+2)^2=5\\\\\Rightarrow x+2=\pm\sqrt5~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{taking square root on both sides}]\\\\\Rightarrow x=-2\pm\sqrt5.$

Thus, the required solution of the given quadratic equation is

$x=-2\pm\sqrt5.$

Option (D) is CORRECT.

Answer 2

−2 ± square root 5 ....................