what two numbers multiply to -30 and add to -3

Question

the x method

Answer 1

If x is one of the numbers, the other is -3-x, because x-3-x=-3, the sum of the numbers.

So when multiplied together we get x(3+x)=-(-30)=30.

Therefore, x²+3x-30=0. We can write this as x²+3x+9/4-9/4-30=0.

(x+3/2)²=30+9/4=129/4, so x+3/2=±√129/2=±5.6789. From this we get x=4.1789 or -7.1789 approx. The two answers are actually the two numbers: 4.1789-7.1789=-3 and 4.1789×(-7.1789)=-30.