# How do you solve 4x^2+8x+3?

Aug 19, 2015

The solutions are:
 color(blue)(x=-3/2

color(blue)(x=-1/2

#### Explanation:

$4 {x}^{2} + 8 x + 3$ , solving assuming that the expression is equated to zero.

$4 {x}^{2} + 8 x + 3 = 0$

We can Split the Middle Term of this expression to factorise it and thereby find solutions.

In this technique, if we have to factorise an expression like $a {x}^{2} + b x + c$, we need to think of 2 numbers such that:

${N}_{1} \cdot {N}_{2} = a \cdot c = 3 \cdot 4 = 12$
and
${N}_{1} + {N}_{2} = b = 8$

After trying out a few numbers we get ${N}_{1} = 2$ and ${N}_{2} = 6$
$2 \cdot 6 = 12$, and $2 + 6 = 8$

$4 {x}^{2} + 8 x + 3 = 4 {x}^{2} + 2 x + 6 x + 3$

$4 {x}^{2} + 2 x + 6 x + 3 = 2 x \left(2 x + 1\right) + 3 \left(2 x + 1\right)$

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

Now we equate factors to zero.
2x+3=0, color(blue)(x=-3/2

x+2=0,color(blue)(x=-1/2