Solved example of quadratic equations
Factor the trinomial $2x^2-7x+3$ of the form $ax^2+bx+c$, first, make the product of $2$ and $3$
Now, find two numbers that multiplied give us $6$ and add up to $-7$
Rewrite the original expression
Factor $2x^2-6x-x+3$ by the greatest common divisor $2$
Factor the polynomial $\left(x^2-3x\right)$ by it's greatest common factor (GCF): $x$
Factoring by $x-3$
Break the equation in $2$ factors and set each equal to zero, to obtain
Solve the equation ($1$)
We need to isolate the dependent variable $x$, we can do that by simultaneously subtracting $-3$ from both sides of the equation
Canceling terms on both sides
$x+0=x$, where $x$ is any expression
Canceling terms on both sides
Solve the equation ($2$)
We need to isolate the dependent variable $x$, we can do that by simultaneously subtracting $-1$ from both sides of the equation
Canceling terms on both sides
$x+0=x$, where $x$ is any expression
Multiply $-1$ times $-1$
Canceling terms on both sides
Divide both sides of the equation by $2$
Simplifying the quotients
Combining all solutions, the $2$ solutions of the equation are
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