What is a solution to (x-3)(x+9)=-27

Accepted Solution

Answer:-6 0Step-by-step explanation:By observation we can see one solution is x=0 since this will give us (0-3)(0+9)=(-3)(9)=-27 which is the result on the right hand side.Now this is a quadratic equation so it should have another solution. This one doesn't seem as obvious to me.The goal normally is to get 0 on side and factor if possible or use quadratic formula.  There is also completing the square.So I'm going to multiply (x-3)(x+9) using foil.First: x(x)=x^2Outer: x(9)=9xInner: -3(x)=-3xLast: -3(9)=-27---------------------Combine like terms:x^2+6x-27So the equation is:x^2+6x-27=-27Add 27 on both sides:x^2+6x+0=0x^2+6x=0Factor x out:x(x+6)=0In order for these equation to be true one of the left hand factors need to be 0.Let's find when x is 0, well that is when x=0.Let's find when x+6 is 0.x+6=0 can be solved by subtracting 6 on both sides:x=-6The solutions are -6 and 0.We already checked x=0.Let's check x=-6:Plugging in -6 where x is in the given equation:(-6-3)(-6+9)(-9)(3)-27 which is the same as right hand side.