Express 2x^2+8x+3 in the form 2 (x+p) ^2+q

2 (x + 2) ² - 5

Step-by-step explanation:

Given

2x² + 8x + 3

To obtain the required form use the method of completing the square.

The coefficient of the x² term must be 1, thus factor 2 out of 2x² + 8x

= 2 (x² + 4x) + 3

add/subtract (half the coefficient of the x - term) ² to x² + 4x

= 2 (x² + 2 (2) x + 4 - 4) + 3

= 2 (x + 2) ² - 8 + 3

= 2 (x + 2) ² - 5

with p = 2 and q = - 5