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Find all values of $x$ such that $x^2 - 5x + 4 = -x^2 - 25x - 14$. If you find more than one value, then list your solutions, separated by commas.

 May 28, 2024

Best Answer 

 #1
avatar+806 
+1

First off, let's move all terms to one side and combine all like terms. 

 

We get \(2x^2+20x+18=0\). Simplifying, we get \(x^2+10x+9 = 0\)

 

Now, let's note that this quadratic can be factored! Putting it into factored form, we get \((x+1)(x+9)=0\)

 

This gets us the values of \(x = -1, -9\)

 

Check your answers and make sure they work. These do if we plug them back in!

 

Thanks! :)

 May 28, 2024
 #1
avatar+806 
+1
Best Answer

First off, let's move all terms to one side and combine all like terms. 

 

We get \(2x^2+20x+18=0\). Simplifying, we get \(x^2+10x+9 = 0\)

 

Now, let's note that this quadratic can be factored! Putting it into factored form, we get \((x+1)(x+9)=0\)

 

This gets us the values of \(x = -1, -9\)

 

Check your answers and make sure they work. These do if we plug them back in!

 

Thanks! :)

NotThatSmart May 28, 2024

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