Completing the square help needed?

1st problem:
2x² + 16x = 0
x² + 8x = 0
x² + 4x = 4²
(x + 4)² = 16
x + 4 = 4

x = 4 - 4, x = 0
x = - 4 - 4, x = - 8

Answer: x = 0, - 8; Factors: 2x(x + 8)

2nd problem:
3x² = 24x
x = 8

Answer: x = 0, 8; Factors: 3x(x - 8)

a) 2x² +16x

2x² + 16x =

Group.
(2x² + 16x) =

Factor
2(x² + 8x) =

Add placeholders.
2(x² + 8x + ___) - 2(___) =

Notice that the second blank is multiplied by -2 to account for what you had to add to complete the square.

Take the coefficient of the x term: 8
Divide it by 2: 8 / 2 = 4
Square it: (4)² = 16

Add 16 to both blanks.
2(x² + 8x + 16) - 2(16) =

x² + 8x + 16 is the expanded form of a perfect square binomial.

Remember that (a + b)² = a² + 2ab + b². Apply this to what you have.
2(x² + 8x + 16) - 2(16)
2(x + 4)² - 2(16)

Simplify the rest.
2(x + 4)² - 32

ANSWER: 2(x + 4)² - 32 <== completed square

b) 3x² - 24x

3x² - 24x =

Group.
(3x² - 24x) =

Factor
3(x² - 8x) =

Add placeholders.
3(x² - 8x + ___) - 3(___) =

Notice that the second blank is multiplied by -3 to account for what you had to add to complete the square.

Take the coefficient of the x term: -8
Divide it by 2: -8 / 2 = -4
Square it: (-4)² = 16

Add 16 to both blanks.
3(x² - 8x + 16) - 3(16) =

x² - 8x + 16 is the expanded form of a perfect square binomial.

Remember that (a - b)² = a² - 2ab + b². Apply this to what you have.
3(x² - 8x + 16) - 3(16) =
3(x - 4)² - 3(16) =

Simplify the rest.
3(x - 4)² - 48

ANSWER: 3(x - 4)² - 48 <== completed square

Part a)
2 ( x ² + 8x )
2 ( x ² + 8x + 16) - 32
2 ( x + 4 ) ² - 32

Part b)
3 ( x ² - 8x )
3 ( x ² - 8x + 16) - 48
3 ( x - 4 ) ² - 48

a) firstly divide the equation by 2 so you get
x^2 + 8x
then u factorise the equation so u get
x(x+8)
therefore x=o or x= -8

b) again divide the equation by 3 so you get
x^2 - 8x
then u factorise the equation so u get
x(x-8)
therefore x=0 or x= 8

hope this helps

a)
2x^2 + 16x
= x^2 + 8x + ?
= x^2 + 4x + 4x + ?
............↳.....↳ 4^2 = 16
= x^2 + 4x + 4x + 16
= x^2 + 8x + 16

b)
3x^2 - 24x
= x^2 - 8x + ?
= x^2 - 4x - 4x + ?
...........↳....↳ (-4)^2 = 16
= x^2 - 4x - 4x + 16
= x^2 - 8x + 16

a) 2x² +16x
2(x² +8x +16 - 16)
2(x+4)^2 - 32

b) 3x² - 24x
3(x² - 8x + 16 - 16)
3(x-4)^2 - 32

a) x^2+8x+16
b)x^2-8x+16

a) this equation a is may be

2X^2+15X

add a square to the equation

2X^2+15X+25=0...............25 is the square you added

factor this equation
(2X+5)(X+5)

b) 3x^2-24x is may be
3x^2+24x -------------------- in order that it will have a square

3x^2+24x+36=0....................where 36 is the square

factor the equation or find the roots

(3x+6) (x+6)=0