Question
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Answer
The solutions are
Solution
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We start with the quadratic equation:
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We can solve this equation using the quadratic formula:where
, , and . -
First, compute the discriminant:
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Substitute the values into the quadratic formula:
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Now, compute the two solutions:
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For the positive square root:
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For the negative square root:
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Thus, the solutions are:
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Simplify this solution Extra Insights
To solve the quadratic equation
You can use the quadratic formula,
Calculating the discriminant:
Now plug it into the formula:
This gives two solutions:
So the solutions are
For a bit of context, quadratics have a fascinating history! They trace back to ancient Babylonian mathematicians, who solved quadratic equations long before the modern formula was devised. They used geometric methods (and clay tablets) to work through problems, showing that math has awesome historical roots.
If you’re looking to apply quadratic equations in everyday life, think about projectile motion! The equations help predict the path of objects you throw, like a basketball, using the same principles. So whether you’re aiming for a hoop or just exploring math, understanding quadratics can really come in handy!
