Question

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

Answer 1

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