Asked by Smartypants
Solve the equation using a table.x squared minus 11 x plus 24equals0Question content area bottomPart 1xequalsenter your response here(Use a comma to separate answers as needed.)
Answers
Answered by
GPT-4o mini
To solve the equation \( x^2 - 11x + 24 = 0 \) using a table, we can factor the quadratic expression.
First, we can look for two numbers that multiply to 24 (the constant term) and add up to -11 (the coefficient of the linear term). The numbers that meet these criteria are -3 and -8, since:
\[
-3 \times -8 = 24
\]
\[
-3 + (-8) = -11
\]
Thus, we can factor the equation as:
\[
(x - 3)(x - 8) = 0
\]
Now, we can set each factor to zero to find the solutions:
1. \( x - 3 = 0 \) → \( x = 3 \)
2. \( x - 8 = 0 \) → \( x = 8 \)
So the solutions to the equation \( x^2 - 11x + 24 = 0 \) are \( x = 3 \) and \( x = 8 \).
Using a comma to separate the answers, we have:
\[
x = 3, 8
\]
First, we can look for two numbers that multiply to 24 (the constant term) and add up to -11 (the coefficient of the linear term). The numbers that meet these criteria are -3 and -8, since:
\[
-3 \times -8 = 24
\]
\[
-3 + (-8) = -11
\]
Thus, we can factor the equation as:
\[
(x - 3)(x - 8) = 0
\]
Now, we can set each factor to zero to find the solutions:
1. \( x - 3 = 0 \) → \( x = 3 \)
2. \( x - 8 = 0 \) → \( x = 8 \)
So the solutions to the equation \( x^2 - 11x + 24 = 0 \) are \( x = 3 \) and \( x = 8 \).
Using a comma to separate the answers, we have:
\[
x = 3, 8
\]