Question

Solve the equation by completing the square: x2 + 8 = 6x
Enter the smallest of the two zeros. Use a number only.

Answer 1

\[x^2-6x=-8\]

Answer 2

Add 9 to both sides.

Answer 3

(x^2-6x+9) = 1

Answer 4

(x-3)^2 = 1

Answer 5

\[x^2-6x+9=1\]
\[(x-3)^2=1\]

Answer 6

Take the square root of both sides.

Answer 7

x-3 =+- 1

Answer 8

\[x-3=\pm1\]

Answer 9

x=3+- 1

Answer 10

This can be re-arranged to get x^2 - 6x +8 = 0.

Factorise to get (x-2)(x-4). So x = 2 and 4.

The smallest of the two roots is 2.

I know this can be solved by completeing the square, but it is much easier to factorise!!! Only complete the square when the discriminant of the quadratic is not more than zero.

Answer 11

\[x=4 \]
\[x=2\]

Answer 12

2 is correct