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2 votes
Solve by completing the square.

j² + 14j + 5 = 0
Write your answers as integers, proper or improper fractions in simplest form, or decimals
rounded to the nearest hundredth.
Submit
or j =
=

1 Answer

4 votes

Answer:


j = 7 \pm √(44)

Explanation:

First, move the constant term to the other side of the equation.


j\² + 14j + 5 = 0


j\² + 14j = -5

Next, add the coefficient of the first degree j term divided by 2, then squared to both sides.


j^2 + 14j + (14/2)^2 = -5 + (14/2)^2


j^2 + 14j + (7)^2 = -5 + (7)^2


j^2 + 14j + 49 = -5 + 49


j^2 + 14j + 49 = 44

Now, we can factor the left side as a square.


(j+7)(j+7) = 44


(j+7)^2 = 44

Finally, we can take the square root of both sides to solve for j.


√((j+7)^2) = \sqrt{44


j+7=\pm√(44)


\boxed{j = 7 \pm √(44)}

Note that there are two solutions, as
\sqrt{44 could be positive OR negative because of the even root property:

if
x^2 = a^2,

then
x = \pm a

because both
(+a)^2 and
(-a)^2 equal
a^2.

User AnotherUser
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7.7k points

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