5 months ago
Q:

3x^2+x-4=0

Accepted Solution

A:

Solution variant #6.

Write $x$ as a difference
$3{x}^{2}+4x-3x-4=0$
Factor out $x$ from the expression
$x \times \left( 3x+4 \right)-3x-4=0$
Factor out the negative sign from the expression
$x \times \left( 3x+4 \right)-\left( 3x+4 \right)=0$
Factor out $3x+4$ from the expression
$\left( 3x+4 \right) \times \left( x-1 \right)=0$
When the product of factors equals $0$, at least one factor is $0$
$\begin{array} { l }3x+4=0,\\x-1=0\end{array}$
Solve the equation for $x$
$\begin{array} { l }x=-\frac{ 4 }{ 3 },\\x-1=0\end{array}$
Solve the equation for $x$
$\begin{array} { l }x=-\frac{ 4 }{ 3 },\\x=1\end{array}$
The equation has $2$ solutions, so we'll label them as $x_1$ and $x_2$
$\begin{align*}&\begin{array} { l }x_1=-\frac{ 4 }{ 3 },& x_2=1\end{array} \\&\begin{array} { l }x_1\approx-1.33333,& x_2=1\end{array}\end{align*}$