I have to following problem: $$q²+3q=40$$.
The anwser is $q=5$ and $q= −8$ can someone give me the steps?
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6Have you tried googling "quadratic equations" or something similar? You should be able to find tons of information online. – Matti P. Mar 29 '21 at 11:15
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1Welcome to MSE. Please read this text about how to ask a good question. – José Carlos Santos Mar 29 '21 at 11:20
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1See the Wikipedia Quadratic Equation article. – user2661923 Mar 29 '21 at 12:05
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The quick version is to first move everything to one side:
$$q^2+3q-40=0$$
From here, you can factor if you can spot the factors by inspection or if you have difficulty with that you can rely on the quadratic formula. The above is in the form $aq^2+bq+c=0$ where $a=1,~b=3,~c=-40$ which has roots $\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}$. Plugging in the values gives
$$\dfrac{-3\pm\sqrt{3^2-4\cdot 1\cdot (-40)}}{2\cdot 1} = \dfrac{-3\pm \sqrt{169}}{2}=\dfrac{-3\pm 13}{2}$$
which gives roots $5$ and $-8$, as expected.
JMoravitz
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