Question

Solve by completing the square:

7x + 2 = −3x²

Answer 1

Given:

7x + 2 = −3x²

3x² + 7x + 2 = 0

Divide the whole equation by 3:

`x^2 + 7/3x +2/3 = 0`

`x^2 + 7/3 x = -2/3`

Take half of the coefficient of x and square it:

Coefficient of x = `7/3`

Half = `7/6`

Square = `(7/6)^2 = 49/36`

`x^2 + 7/3 x + 49/36 = -2/3 + 49/36`

`-2/3 = -24/36`

`=> -24/36 + 49/36 = 25/36`

`= (x+7/6)^2 = 25/36`

`x + 7/6 = +-5/6`

Case 1:

`x = -7/6 + 5/6 = -2/6 = -1/3`

Case 2:

`x = -7/6 - 5/6 = -12/6 = -2`

`x = -1/3 or x = -2`