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# help algebra

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Find the smallest value of x such that x^2 + 10x + 25 = $$18$$

Jan 23, 2022

#1
+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
+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 = $$-5 - 3\sqrt{2}$$

Jan 23, 2022