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.

RedDragonl May 28, 2024

#1**+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! :)

NotThatSmart May 28, 2024

#1**+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