Question

Solve by completing the square:

3x² − 5x − 1 = 0

Answer 1

Given:

3x² − 5x − 1 = 0

Move the constant to the right-hand side

3x² − 5x = 1

Make the coefficient of x² equal to 1

`x^2 - 5/3x = 1/3`

Complete the square

Coefficient of x = `-5/3`

Half = `-5/6`

Square = `(5/6)^2 = 25/36`

`x^2 - 5/3x + 25/36 = 1/3 + 25/36`

`1/3 = 12/36`

`=> 12/36 + 25/36 = 37/36`

`(x-5/6)^2 = 37/36`

`x - 5/6 = +- sqrt(37/36) = +- sqrt37/6`

`x = 5/6 +- sqrt37/6`

`x = (5+-sqrt37)/6`