Question

Solve by completing the square method 3x²=15-4x ​

Answer 1

x = - 3, x =
`(5)/(3)`

Explanation:

Given

3x² =15 - 4x ( add 4x to both sides )

3x² + 4x = 15 ← factor out 3 from each term on the left side

3(x² +
`(4)/(3)` x) = 15

To complete the square

add/subtract ( half the coefficient of the x- term)² to x² +
`(4)/(3)` x

3(x² + 2(
`(2)/(3)` )x +
`(4)/(9)` -
`(4)/(9)` ) = 15

3(x +
`(2)/(3)` )² -
`(4)/(3)` = 15 ( add
`(4)/(3)` to both sides )

3(x +
`(2)/(3)` )² = 15 +
`(4)/(3)` =
`(49)/(3)` ( divide both sides by 3 )

(x +
`(2)/(3)` )² =
`(49)/(9)` ( take the square root of both sides )

x +
`(2)/(3)` = ±
`\sqrt{(49)/(9) }` = ±
`(7)/(3)` ( subtract
`(2)/(3)` from both sides )

x = -
`(2)/(3)` ±
`(7)/(3)`, then

x = -
`(2)/(3)` -
`(7)/(3)` = - 3

x = -
`(2)/(3)` +
`(7)/(3)` =
`(5)/(3)`

Answer 2

Explanation:

3x²=15-4x

divide by 3 on both sides

x²=5-
`(4)/(3)`x ​ ​

move everything to one side

x²+
`(4)/(3)`x ​-5 = 0

add the square of 1/2 the middle term of
`(4)/(3)` but also subtract it too

x²+
`(4)/(3)`x +
`( (2)/(3) )^(2)`​-5-
`( (2)/(3) )^(2)`​ = 0

now use the property of a perfect square to rewrite

`(x+(2)/(3)) ^(2)` -5 -
`(4)/(9)` = 0

rewrite 5 as a fraction

`(x+(2)/(3)) ^(2)` -
`(45)/(9)`-
`(4)/(9)` = 0

add up the fractions

`(x+(2)/(3)) ^(2)` -
`(49)/(9)` = 0

move to the other side

`(x+(2)/(3)) ^(2)` =
`(49)/(9)`

take the square root of both sides :P

`\sqrt{((x+(2)/(3)) ^(2) }` =
`\sqrt{(49)/(9) }`

much easier looking now, just use algebra to solve for x

x +
`(2)/(3)` =
`(7)/(3)`

subtract
`(2)/(3)` from both sides

x +
`(2)/(3)` -
`(2)/(3)` =
`(7)/(3)` -
`(2)/(3)`

x =
`(5)/(3)`

:)

​