Question

How do you solve `x^2-4x-7=0`?

Answer 1

`x = 5.317 or x = -1.317`

Explanation:

This is a quadratic equation. There are 3 methods for solving them:
Factorise, completing the square or using the quadratic formula.

The given equation does not factorise, so option 1 falls away.

My choice would be completing the square because:
the coefficient of `x^2` is 1, and the coefficient of the middle term is even,

Student often think completing the square is difficult, but in a case like this it is quicker and easier than using the formula.

`x^2 - 4x -7 = 0`
Move the constant to the RHS: `x^2 - 4x " " = 7`

Add on the square of, half of the middle coefficient to both sides:
`( 4÷ 2 = 2 and 2^2 = 4)`

`x^2 - 4x + color(red)4 = 7 + color(red)4`

The LHS is now the square of a binomial

`(x - 2)^2 = 11 " "` Now find the square root of each side

`x - 2 = +-sqrt11 " "` Solve for x twice.

`x = sqrt11 + 2 " " or x = -sqrt11 + 2`

`x = 5.317 " " or x = -1.317`