In Exercises 35–46, determine the constant that should be added t...

Question

In Exercises 35–46, determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial.

x^2 + 3x

Accepted Answer

Hello. Everyone in this video we're going to be looking at this practice problem where we want to complete the square for the equation P squared plus 23 P. So recall that if we have an equation binomial equation in the form X squared plus B. X. Then we complete the square by adding B divided by two squared. So in this case our equation P squared plus 23 P follows that binomial form. So we're going to be adding B divided by two squared and in this case B is equal to 23. So we're gonna have P squared plus 23 P plus B- 23 divided by two squared. And notice how we've just added a completely new number to our equation. So we need to account for that by subtracting that number. So I'm going to put the equation p squared plus 23 P plus divided by two squared in a parentheses. And outside of that I'm going to add or subtract what I've just added. So I'm gonna subtract 23 divided by two squared and now you can see that positive and negative. 23 divided by two squared, cancel each other out to give us zero. So it's like we've added no new numbers into our equation because we don't want to change the values of our equations. We just want to complete the square. So now that I've completed the square in my parentheses I can factor this to bp plus 23 divided by two squared. And then I still have the minus 23 divided by two squared on the outside. So now you can see that my equation has become a factored version where I have P plus 23 divided by two squared. So now I can also simplify the 23 divided by two squared. I do that. I have 23 divided by two times 23 divided by two and that is equal to 529 divided by four. So I can plug that back in. So my final equation is P plus 23 divided by two squared -529, divided by four. So this becomes my final equation for when I complete the square. And you can see that this aligns with answer choice B. And you can see A. Is very similar except that there is a plus where we know that needs to be negative And C&D don't take into account that 23 divided by two needs to be squared because that's the number that we added inside of the parentheses. So hopefully this video helped and see you next time

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