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Quadratics can be solved in different ways.
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We learned how to solve them by factorizing and by completing the square in these videos.
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We're now going to discover how to solve quadratics using the quadratic formula.
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Quadratics can't always be factorized,
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but the quadratic formula does always work.
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Factorizing is easier to do, so it's better to check that out first.
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However, if you can't factorize,
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then we can use the quadratic formula instead.
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If the question says giving your answer to three significant figures or giving your answer to two decimal places,
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it means these quadratic cannot be factorized.
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So, straight away, look to use a quadratic formula.
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So let's have a look at how to use a quadractic formula to solve quadratics.
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Firstly, make sure your quadratic equals 0.
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Then "a" is the number in front of the "x2",
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"b" is the number in front of the "x",
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and "c" is a number on its own.
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Make sure you keep the sign in front of the numbers.
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And then, we just substitute the values into the formula.
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Let's have a look at an example.
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"a" is +2, "b" is -3, and "c" is -4.
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And then just substitute these numbers into the formula.
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Minus -3 "plus or minus" the "square root" of -3 squared
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Minus 4 "multiplied by" 2 "multiplied" by -4.
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All of that "divided by" 2 "multiplied by" 2.
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Be very careful with the negatives.
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Use bracket to prevent mistakes.
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We can either type that straight into our calculator.
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So "minus" -3 "plus" everything for one answer,
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and then to get the second answer, type in "minus" -3 "minus" everything.
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Or we can simplify it a bit further.
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3 "plus or minus" the "square root" of 41, all "divided by" 4.
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And then type this into a calculator.
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From your calculator, you should get x equals 2.35,
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and x equals -0.851.
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So you can choose to jump straighten and use your calculator here.
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Or you can simplify it a little bit further and then use your calculator.
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Either way, just be really careful with negatives.
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So here are a few for you to do.
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Remember to use brackets to help with negatives.
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We know that we need to use a quadratic formula because it tells us to round our answer.
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For "b", make sure the quadratic equals 0 before you start.
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Pause the video, work them out, and click play when you're ready.
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How'd you go on?
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If you made a mistake, go back and check your negatives.
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This is usually where mistakes are made.
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So there we have solving quadratics using the quadratic formula.
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"a" ,"b", and "c" are just the coefficients from the equation,
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and we substitute these numbers straight into the formula.
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Take your time, and just be careful with negatives.