Question

Solve for x:

$4x^2+14x+6=0$

Answer 1

Roots of quadratic equations:

$4x^2+14x+6=0$ (divide the equation by $2$)

$\Rightarrow$ $2x^2+7x+3=0$

$\Rightarrow$ $2x^2+6x+x+3=0$ (using factorization method)

$\Rightarrow$$2x(x+3)+1(x+3)=0$

$\Rightarrow$ $\left(2x+1\right)\left(x+3\right)=0$

$$\begin{gathered} \Rightarrow \left(2x+1\right)=0or\left(x+3\right)=0 \\ x=\frac{-1}{2}orx=-3 \end{gathered}$$

Hence, the value of $x$ are $-3,\frac{-1}{2}$.