Question

Rewrite the function by completing the square

F(x)=x^2+6x-78

F(x)=(x+?)^2+?

Answer 1

The expression after completing the square is:

`f(x) = (x+3)^(2) -87`

Explanation:

The function is rewritten after making algebraic manipulation:

`f(x) = x^(2) + 6\cdot x +9 - 9 - 78`

The expression after completing the square is:

`f(x) = (x+3)^(2) -87`

Answer 2

F(x) = (x + 3)^2 -87

Explanation:

Here, we want to rewrite the function by completing the square.

Firstly, we move the c term(-78) to the right hand side of the equation and that becomes

x^2 + 6x = 78

Then, we can complete the square on the right hand side here, to be

Let’s add 9 to both sides

That would be;

x^2 + 6x + 9 = 78 + 9

x^2 + 6x + 9 = 87

(x+3)^2 = 87

or simply

(x+3)^2 -87 = 0

So our F(x) becomes

F(x) = (x + 3)^2 -87