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Answer:
-3
Step-by-step explanation:
This is a quadratic equation. Therefore, one way we can solve this is by using the quadratic formula, [tex]\frac{-b+\sqrt{b^2-4ac} }{2a}[/tex] and [tex]\frac{-b-\sqrt{b^2-4ac} }{2a}[/tex].
a, b, and c represent the coefficients in our equation [tex]x^2-5x-24=0[/tex]. 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: [tex]\frac{-b+\sqrt{b^2-4ac} }{2a}[/tex]
[tex]\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[/tex]
Oops! We are looking for the other solution. Let us plug in the values in this equation instead: [tex]\frac{-b-\sqrt{b^2-4ac} }{2a}[/tex]
[tex]\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[/tex]
I hope this helps! Let me know if you have any questions :)