Question

If using the method of completing the square to solve the quadratic equation
X2 – 192
3 = 0, which number would have to be added to "complete the
square"?

Help please

Answer 1

Answer:

The number that would be added to make $x^2-19x-3=0$ a complete square is $\mathbf{(\frac{19}{2})^2}$

Step-by-step explanation:

We need to solve the expression $x^2-19x-3=0$ using completing the square method.

Completing square method is of form: $(a-b)^2=a^2-2ab+b^2$

We need to find the term, that it a complete square

The middle term is -19x so, it can be made as: -2(x)(19/2) according to the formula a^2-2ab+b^2

We have a=x and b=19/2

So, adding and subtracting (19/2)^2

$x^2-2(x)(\frac{19}{2} )+(\frac{19}{2})^2- (\frac{19}{2})^2-3=0\\(x-\frac{19}{2})^2-\frac{361}{4}-3=0$

So, the number that would be added to make $x^2-19x-3=0$ a complete square is $\mathbf{(\frac{19}{2})^2}$