Question

Bao yu is completing the square to solve the polynomial epuation

X^2-x-3=0.
What should her first step be ?

Answer 1

The first step would be to add 3 on both sides of the equation.

Explanation:

Given a polynomial or a quadratic equation, the first step in completing the square is to take the constant term to the other side of the equation. In the polynomial given the constant term is -3 which implies that we can add 3 on both sides of the equation in order to eliminate this constant term from the left hand side;

x^2 -x -3 +3 = 0 + 3

x^2 - x = 3

Answer 2

The first step of Bao yu is to isolate the constant

Explanation:

For using completing the square to solve the polynomial equation, the equation should be of the type
`a^2 \pm 2ab +b^2` that can also be written as:
`(a\pm b)^2`

so, for the given equation:
`x^2 -x -3 =0`

The first step should be to isolate the constant:

`x^2 -x = 3`

Then we have to make the middle term according to 2ab where a = 1x and b= (1/2) i.e, -2(1x)(1/2) = 1x

so,by adding (1/2)^2 on both sides of equation, we can complete the formula:

`x^2 -x = 3`

`x^2 -2(x)((1)/(2)) + ((1)/(2))^2 = 3 ((1)/(2))^2`

Solving we get,

`(x- ((1)/(2)))^2 = 13/4`

So, the first step is to isolate the constant.