Question

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.

Answer 1

-23.18, -.82

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

Answer 2

-23.18, -0.82

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