How would I solve x^2 + 7x + 10 = 0

The first step of solving this equation to find out what x is, is to factorise it.

This means grouping it into a set of double brackets which will take the form (x+a)(x+b)=0.

The a and the b must give the coefficient of x (7 in this case) when added, and the units (10 in this case) when multiplied.

Thinking of the pairs of factors for 10 (10 & 1, 5 & 2) we can see that the only pair that adds to 7 is 5 and 2.

Therefore our factorised equation looks like this:


If you want to check that this is right, try multiplying out the terms to see if you get back to the equation we started with.

From here we can get our solutions.

For the equation to be right, one of the sets of brackets must be zero, meaning:

x+5 = 0; and x+2 = 0; are both correct.

The last step is simply to rearrange these two equations to make x the subject.

The first gives us x = -5 and the second x = -2

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