Question

12. Solve x^2 + 6x - 16 = 0 by completing the square.


Please help and show work

Answer 1

x is 2 and -8

Explanation:

`{x}^(2) + 6x - 16 = 0`

general equation

`{ax}^(2) + (sum)x + product = 0`

sum is 6, product is -16

for completing squares,

first divide the sum by 2:

`= (6)/(2) = 3`

add the square of the result on (x² + 6x) and subtract it from the product:

`( {x}^(2) + 6x + {3}^(2) ) - 16 - {3}^(2) = 0 \\ {(x + 3)}^(2) - 25 = 0 \\ {(x + 3)}^(2) = 25`

take square root:

`\sqrt{ {(x + 3)}^(2) } = √(25 ) \\ x + 3 = ±5 \\ x = ±5 - 3`

x is either: 5-3 or -5-3

`x = 2 \: \: and \: - 8`