Question

X^2 + 11x= -28
Solutions of quadratic equation

Answer 1

\[x^2+11x+28=0\]
1*28=28
4+7=11
4*7=28
write 11x=4x+7x and make factors.

Answer 2

To pan it out a bit more. You need to get all the numbers on 1 side so the equation is equal to 0. So you add 28 to boths sides to get
\[x ^{2} +11x + 28 = 0\] Now we need to find a pair of numbers that add to make 28 and multiply to make 11.
As surji pointed out, 7x4 = 28 and they also add to make 11 so 7 and 4 and the numbers we want.

Now we can because the X^2 term has a coefficent we can put these numbers straight into factors.

(x+7)(x+4). This bracked when multiplied out will give the quadratic sown above.

But beacuse the equation is = to 0 we now need to work out what x has to be for this to equal 0. So (x+7)(x+4) = 0

If x was -7 let's say, then we would end up with 0 x -3 and 0 times anything = 0 so -7 works.

and if x was -4 the same would happen so -4 and -7 are the answers.