Now, we have a quadratic equation in the form ax^2 + bx + c = 0 where a = -13, b = 13, and c = 24. We can solve this equation using the quadratic formula:
x = [-b ± sqrt(b^2 - 4ac)] / 2a
Plugging in the values, we get:
x = [-13 ± sqrt(13^2 - 4(-13)(24))] / 2(-13) x = [-13 ± sqrt(169 + 624)] / -26 x = [-13 ± sqrt(793)] / -26
Therefore, the solutions are:
x = [-13 + sqrt(793)] / -26 and x = [-13 - sqrt(793)] / -26.
First, we can combine like terms:
(x^2 - x) - 14(x^2 - x) + 24
= x^2 - x - 14x^2 + 14x + 24
= -13x^2 + 13x + 24
Now, we have a quadratic equation in the form ax^2 + bx + c = 0 where a = -13, b = 13, and c = 24. We can solve this equation using the quadratic formula:
x = [-b ± sqrt(b^2 - 4ac)] / 2a
Plugging in the values, we get:
x = [-13 ± sqrt(13^2 - 4(-13)(24))] / 2(-13)
x = [-13 ± sqrt(169 + 624)] / -26
x = [-13 ± sqrt(793)] / -26
Therefore, the solutions are:
x = [-13 + sqrt(793)] / -26 and x = [-13 - sqrt(793)] / -26.