Question

How do you solve `2x^2 – 28x + 84 = 0` using completing the square?

Answer 1

Logical first step is dividing everything by `2`

Explanation:

`->x^2-14x+42=0`

Take half the `x`-coefficient and square that:
`x^2-14x+(-7)^2=x^2-14x+49=(x-7)^2`

If we write the original `42=49-7`:
`->(x-7)^2-7=0->(x-7)^2=7`

So: `x-7=sqrt7->x=7+sqrt7`
Or: `x-7=-sqrt7->x=7-sqrt7`

Often written as `x_(1,2)=7+-sqrt7`