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Find the smallest value of x such that x^2 + 10x + 25 = 64.

 Jul 13, 2021
 #1
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+3

Answer: \(3\)

 

There are two ways to do this.

 

Way 1:

 

The number is obviously going to be small. 

Guessing 1: Left side is 36

Guessing 2: Left side is 49

Guessing 3: Left side is 64

 

3 is the answer.

 

Way 2: 

 

Way 1 would not have worked if the number was not an integer, or if it were larger. Factoring the left side gives (x+5)², and 64 = 8². So, you have x+5=8, which gives the answer x = 3.

 Jul 13, 2021

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