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We want to use the discriminant of the given quadratic equation to determine the number and type of solutions.
In the Quadratic Formula, $b_{2}−4ac$ is the discriminant. $ax_{2}+bx+c=0⇔x=2a-b±b_{2}−4ac $
If we just want to know the **number and type** of solutions, and not the solutions themselves, we only need to work with the discriminant. Let's first write all the terms on the left-hand side.
$x_{2}+7x=-11⇔x_{2}+7x+11=0 $
Having rewritten the equation, we can now identify the values of $a,$ $b,$ and $c.$
$1x_{2}+7x+11=0 $
Finally, let's evaluate the discriminant.
Since the discriminant is $5,$ *greater than* zero, the quadratic equation has **two real** solutions. ### Extra

Further information

If the discriminant is *greater than* zero, the equation will have **two** real solutions. If it is *equal to* zero, the equation will have **one** real solution. Finally, if the discriminant is *less than* zero, the equation will have **no** real solutions.

$b_{2}−4ac$

$>0$

$=0$

$<0$

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