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Find the smallest value of x such that x^2 + 10x + 25 = \(18\)

 Jan 23, 2022
 #1
avatar+2403 
+1

x^2 + 10x + 25 = (x+5)^2

(x+5)^2 = 18

(x+5) = +/-sqrt(18)

 

Can you take it from here?

 

=^._.^=

 Jan 23, 2022
 #2
avatar+717 
-4

First we have to turn the equation to a standard quadratic equation: we get

\(x^2 + 10x + 7 = 0\)

 

Now we can apply the quadratic formula. x = \(-b {+\over} \sqrt{b^2 - 4ac}\over2a\) where a is the coefficient of x^2, b is the coefficient of x, and c is the constant.

Plugging in the values, we get x = \(-10 {+\over} 6\sqrt{2}\over2\) for our two solutions of x. 

Since the problem is asking for the smaller value, we take the subtraction operation in the equation above, getting:

 

x = \(-5 - 3\sqrt{2}\)

 

 

smiley

 Jan 23, 2022

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