x² - 5x - 24 = 0
First, we have to solve the quadratic equation and find the two values of x that fit the equation.
[tex]x = \frac{5+- \sqrt{5^{2} + 4*1*24 } }{2*1} = \frac{5+- \sqrt{25 + 96} }{2} = \frac{5+- \sqrt{121} }{2} = \frac{5+-11}{2} [/tex]
There are two values of x that fit:
x₁ = (5+11)/2 = 16/2 = 8
x₂ = (5-11)/2 = -6/2 = -3
Now I can restate the original equation in terms of a product of factors, with this product being equal to zero:
(x - x₁) * (x - x₂) = 0
ANSWER (x-8) * (x+3) = 0
Now I can solve each factor by setting each one equal to zero and solving the resulting linear equations:
x - 8 = 0 or x + 3 = 0
x = 8 or x = -3
We can check that these two values are the solution to the original quadratic equation.
x² - 5x - 24 = 0
First value
8² -5*8 -24 = 0
64 - 40 -24 = 0
0 = 0 ¡Checked!
Second value
(-3)² -5(-3) -24 = 0
9 + 15 -24 = 0
0 = 0 ¡Checked!
Hope this helps!
[tex]\textit{\textbf{Spymore}}[/tex]
