Question

Complete the square to make a perfect square trinomial. Then, write the result as a binomial squared. x2+3/2x

Answer 1

Answer:

The added term needed for that expression to be a square is 9/16.

Step-by-step explanation:

We're provided with two terms, and asked to add an additional term to make this a perfect square.  For this to work, the term needs to be a scalar value that is the square of half the coefficient of the second term.

That coefficient is 3/2, so half of that is 3/4, and its square is 9/16.

If we tack that on the end then, we get:

$x^2 + \frac{3x}{2} + \frac{9}{16}\\=(x + \frac{3}{4})^2$

To confirm the answer, let's expand it and see if we get the original expression:

$(x + \frac{3}{4})^2\\= (x + \frac{3}{4})(x + \frac{3}{4})\\= x^1 + \frac{3x}{4} + \frac{3x}{4} + \frac{9}{16}\\= x^2 + \frac{6x}{4} + \frac{9}{16}\\=x^2 + \frac{3x}{2} + \frac{9}{16}$

So 9/16ths is the scalar that needs to be added on the end.