Question

Find the real and/or imaginary solutions by factoring

7. x^2-11x=-24

8. 3x^3+3x^2=27x

Please show your work!

Answer 1

Here is number 7:

`{x}^(2) - 11x = - 24 \\ {x}^(2) - 11x + 24 = 0 \\ (x - 3)(x - 8) = 0 \\ x = 3 \: and \: 8`
Here is number 8:


`3 {x}^(3) + 3 {x}^(2) = 27x \\ 3 {x}^(3) + 3 {x}^(2) - 27x = 0 \\ 3x( {x }^(2) + x - 9) = 0 \\ x = 0 \: and \: two \: more \: solutions \: shown \: below.`
Use the quadratic formula to find the other two solutions:


`x = \frac{ - 1 + - \sqrt{ {1}^(2) - 4(1)( - 9) } }{2(1)} \\ x = ( - 1 + √(37) )/(2) \\ x = ( - 1 - √(37) )/(2)`