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abruzzese [7]
3 years ago
13

Write the quadratic equation in factored form. Be sure to write the entire equation. x2 - 5x - 24 = 0

Mathematics
1 answer:
Vitek1552 [10]3 years ago
8 0

​x² - 5x - 24 = 0

First, we have to solve the quadratic equation and find the two values of x that fit the equation.​

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}​

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!

​\textit{\textbf{Spymore}}​​​

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To complete the square, add 16 like mentioned earlier. However, we also need to subtract 16 to balance things out:

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