+2447 Let's go through the process again, shall we?
Let x represent one of the numbers. Then 15-x is the other number. Knowing this, the equation becomes \(x(15-x)=63\).
| \(x(15-x)=63\) | Distribute. |
| \(15x-x^2=63\) | Subtract 63 from both sides. |
| \(-x^2+15x-63=0\) | I like to divide by -1 out of habit. |
| \(x^2-15x+63=0\) | In this case, this quadratic cannot be factored. I'll use the quadratic formula here. |
| \(x=\frac{-(-15)\pm\sqrt{(-15)^2-4(1)(63)}}{2(1)}\) | Let's do some simplification here. |
| \(x=\frac{15\pm\sqrt{225-252}}{2}\) | |
| \(x=\frac{15\pm\sqrt{-27}}{2}\) | I see an issue here, do you? This is probably why you were unable to come up with a solution. The square root of -27 results in a nonreal answer. |
This means that no quadratic equation with real solutions can have property aforementioned, which is a sum of 15 and a product of 63.
