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Find all values of  such that . If you find more than one value, then list your solutions, separated by commas.

 Dec 31, 2021
 #1
avatar+675 
+1

I see no values.

 Dec 31, 2021
 #2
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Here is the question: Find all values of x such that x^2 - 8x + 15 = 2x^2 - 12x + 11.  If you find more than one value, then list your solutions, separated by commas.

 Dec 31, 2021
 #3
avatar+675 
+1

x^2 - 8x + 15 = 2x^2 - 12x + 11.

 

\(x^2 - 8x + 15 = 2x^2 - 12x + 11 \mbox{ }| -2x^2 - 12x + 11 \\ -x^2 + 4x + 4 = 0 \mbox{ }| \cdot (-1) \\ x^2 - 4x - 4 = 0 \mbox{ }| + 4 \\ x^2 - 4x = 4 \mbox{ }| + 4 \\ x^2 - 4x + 4 = 8 \\ (x - 2)^2 = 8 \mbox { }| \sqrt{(...)} \\ x - 2 = \pm \mbox{ } 2 \sqrt{2} \mbox{ }| + 2 \\ \boxed{x_1 = 2 + 2\sqrt{2} \\ x_2 = 2 - 2\sqrt{2}}\)

 Dec 31, 2021
 #4
avatar+675 
+1

Sorry, that this took long.

 

\(2 + 2\sqrt{2}, \mbox{ } 2 - 2\sqrt{2}\) .

 Dec 31, 2021

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