Question

One of the solutions to the equation x² - 5x-24 = 0 is 8. What is the other solution?​

Answer 1

X^2 - 5x - 24
(X - 8)(x + 3)
X = 8 and x = -3
Therefore, the other solution is -3.

Answer 2

Answer:

-3

Step-by-step explanation:

This is a quadratic equation. Therefore, one way we can solve this is by using the quadratic formula, $\frac{-b+\sqrt{b^2-4ac} }{2a}$ and $\frac{-b-\sqrt{b^2-4ac} }{2a}$.

a, b, and c represent the coefficients in our equation $x^2-5x-24=0$. a represents the coefficient of the term with degree of 2, which is 1. b represents the coefficient of the term with degree of 1, which is -5. c represents the coefficient of the term with degree of 0, which is -24.

Let us plug them in the equation! Let us start with this one: $\frac{-b+\sqrt{b^2-4ac} }{2a}$

$\frac{5+\sqrt{(-5)^2-4*1*(-24)} }{2} =\\\frac{5+\sqrt{25+96} }{2} =\\\frac{5+\sqrt{121} }{2} =\\\frac{5+11}{2} =\\\frac{16}{2} =\\8$

Oops! We are looking for the other solution. Let us plug in the values in this equation instead: $\frac{-b-\sqrt{b^2-4ac} }{2a}$

$\frac{5-\sqrt{(-5)^2-4*1*(-24)} }{2} =\\\frac{5-\sqrt{25+96} }{2} =\\\frac{5-\sqrt{121} }{2} =\\\frac{5-11}{2} =\\\frac{-6}{2} =\\-3$

I hope this helps! Let me know if you have any questions :)