59.2k views
3 votes
Solve for x.
3x² + 3x - 18 = 0
X = [?], [?]

User Reflux
by
8.3k points

1 Answer

4 votes

Answer:

x=2; x=-3

Explanation:

3
x^(2)+3x-18=0

We can use the method of completing the square to solve (you can also use the quadratic formula):

3(
x^(2)+x)-18=0

We can add
(1)/(4) inside the parentheses because this completes the square, as you will see soon. By adding
(1)/(4) in the parentheses, we are actually adding
(3)/(4) to the equation because everything in the parentheses is multiplied by 3. Therefore, we have to add
(3)/(4) to the other side of the equation to keep both sides equal.

3(
x^(2)+x+
(1)/(4))-18=
(3)/(4)

Add 18 to both sides.

3(
x^(2)+x+
(1)/(4))=
(75)/(4)

Divide by 3 on both sides.

(
x^(2)+x+
(1)/(4))=
(25)/(4)


(x+(1)/(2)) ^(2)=
(25)/(4)

Now, take the square root of both sides. Note that there will be a plus minus because squaring the negative of a number will get the same answer as squaring the positive.

x+
(1)/(2) = ±
\sqrt{(25)/(4)}

x+
(1)/(2)
(5)/(2)

We now have two equations and can solve both.

x+
(1)/(2)=
(5)/(2)

Subtract 1/2 on both sides to get

x=2

and

x+
(1)/(2)=-
(5)/(2)

Subtract 1/2 on both sides to get

x=-3

User Yamass
by
7.7k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories