Which is a solution to the equation?
[tex](x-2)(x+5)=18[/tex]
A. [tex]x=-10[/tex]
B. [tex]x=-7[/tex]
C. [tex]x=-4[/tex]
D. [tex]x=-2[/tex]
Answer (2)
Substitute each given value into the equation ( x − 2 ) ( x + 5 ) = 18 .
Evaluate the expression for each value.
Check if the result equals 18.
The solution is x = − 7 .
Explanation
Understanding the Problem We are given the equation ( x − 2 ) ( x + 5 ) = 18 and four possible solutions: x = − 10 , x = − 7 , x = − 4 , and x = − 2 . We need to determine which of these values satisfies the equation.
Solution Strategy We will substitute each given value of x into the equation and check if the result is equal to 18.
Testing x = -10 Let's test x = − 10 :
( − 10 − 2 ) ( − 10 + 5 ) = ( − 12 ) ( − 5 ) = 60 Since 60 e q 18 , x = − 10 is not a solution.
Testing x = -7 Now, let's test x = − 7 :
( − 7 − 2 ) ( − 7 + 5 ) = ( − 9 ) ( − 2 ) = 18 Since 18 = 18 , x = − 7 is a solution.
Testing x = -4 Next, let's test x = − 4 :
( − 4 − 2 ) ( − 4 + 5 ) = ( − 6 ) ( 1 ) = − 6 Since − 6 e q 18 , x = − 4 is not a solution.
Testing x = -2 Finally, let's test x = − 2 :
( − 2 − 2 ) ( − 2 + 5 ) = ( − 4 ) ( 3 ) = − 12 Since − 12 e q 18 , x = − 2 is not a solution.
Conclusion Therefore, the only solution among the given options is x = − 7 .
Examples
Solving quadratic equations is a fundamental skill in algebra with numerous real-world applications. For instance, engineers use quadratic equations to model the trajectory of projectiles, such as rockets or balls. Architects apply them to design arches and other curved structures. Financial analysts use quadratic equations to model investment growth and predict market trends. By understanding how to solve these equations, you can tackle a wide range of practical problems in various fields.
The solution to the equation ( x − 2 ) ( x + 5 ) = 18 is x = − 7 , as it is the only value that makes the equation true. The other values do not satisfy the equation. Therefore, the answer is − 7 .
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