How do I solve the quadratic equation x^2+4x+3=0

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When solving a quadratic equation like this it is useful to write it in the form (x+a)(x+b)=0, as this is simply saying 'two numbers multiplied together equal zero'. A general rule in maths is that whenever two numbers multiply together to equal zero, either one or both of those numbers equal zero (try multiplying any number you can think of by zero and see what you get!)

The next question is how do I write x^2+4x+3 in the form (x+a)(x+b)? The answer to this is simple, you need to search for two numbers which multiply together to make three, and also add together to make 4. In this case the answer is 3 and 1, so we can re-write our original equation as (x+3)(x+1)=0. Now because this product is equal to zero, we can write that either x+3=0 or x+1=0 (because when a product equals zero either one or both of the numbers being multiplied must be zero).

Starting with x+3=0, subtracting 3 from both sides gives us our first solution: x=-3.

We can now subtract 1 from both sides of x+1=0, giving us our second solution: x=-1.

As you can see, there are two solutions to this equation! If you find this hard to believe, you can check that both solutions are correct by replacing all of the x's in the original equation with each solution in turn, and they should both equal zero!

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