Solve by completing the square.

h2 + 24h + 19 = 0

Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.

-23.18, -.82

Step-by-step explanation:

h^2 + 24h + 19 = 0

Subtract 19 from each side

h^2 + 24h = - 19

Take the coefficient of h

24

Divide by 2

24/2 = 12

Square it

12^2 = 144

Add this to both sides

h^2 + 24h+144 = - 19+144

(h+12) ^2 = 125

Take the square root of each side

sqrt ((h+12) ^2) = ±sqrt (125)

h+12 = ±sqrt (125)

Subtract 12 from each side

h+12-12 = - 12 ±sqrt (125)

h = -12 ±sqrt (125)

h = - 12 - sqrt (125) = - 23.18033989

h = - 12 + sqrt (125) = -.819660113

To the nearest hundredth

-23.18, -.82

-23.18, - 0.82

Step-by-step explanation:

h² + 24h + 19 = 0 h²+2h*12+12²-125=0 (h+12) ²-√125²=0 (h+12+11.18) (h+12-11.18) = 0 (h+23.18) (h+0.82) = 0 h+23.18=0 ⇒ h = - 23.18 h+0.82=0 ⇒ h = - 0.82