Solve for x. (3x-4)^2=16 Use the quadratic formula. Please show steps if you have another way to do this.?

Quadratic formula method:
(3x - 4)^2 = 16
=> 9x^2 - 24x + 16 = 16
=> 9x^2 - 24x = 0
=> x(9x - 24) = 0
=> x = 0 or x = 24/9 = 8/3

Alternate method:
(3x - 4)^2 = 16
=> l 3x - 4 l = 4
=> 3x - 4 = - 4 or 3x - 4 = 4
=> 3x = 0 or 3x = 8
=> x = 0 or 8/3.

Expanding perfect squares:
(a + b)² = a² + 2ab + b²
(a – b)² = a² – 2ab + b²

(3x – 4)² = 16 . . . . . . . . . . . . . . . <- expand
(3x)² – 2(3x)(4) + 4² = 16
9x² – 24x + 16 = 16 . . . . . . . . . . .<- subtract 16 from both sides
9x² – 24x = 0 . . . . . . . . . . . . . . . <- factor out 3x
3x(3x – 8) = 0
x = 0, 8/3


Done

(3x - 4)^2 = 16
(3x - 4)(3x - 4) - 16 = 0
9x^2 - 12x - 12x + 16 - 16 = 0
9x^2 - 24x + 0 = 0
x = [-b ±√(b^2 - 4ac)]/2a

a = 9
b = -24
c = 0

x = [24 ±√(576 - 0)]/18
x = [24 ±√576]/18
x = [24 ±24]/18

x = [24 + 24]/18
x = 48/18
x = 8/3

x = [24 - 24]/18
x = 0/18
x = 0

∴ x = 8/3, 0

3 x - 4 = ± 4

3 x = 8 , 3 x = 0

x = 8 / 3 , x = 0

(3x-4)^2=4^2
taking roots on both sides
3x-4=4
3x=4+2=8
x=8/3
x=2.67

quadratic eqation
9x^2-24x+16=16
9x^2-24x=0
3x(3x-8)=0
x=0 or x=8/3

First i FOIL it.

9x^2 - 24x + 16 = 16

9x^2 - 24 + 16 - 16 = 16 - 16 (i'm subtracting the 16 from the right side)

9x^2 - 24x = 0

a = 9
b = -24
c = 0

-b±√(b^2 - 4ac)/ 2a

-(-24) ± √((-24)^2 - 4(9)(0)) / 2(9)

24 ± √((-24)^2 - 0)/ 18

24 ± √576 / 18

24± 24
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18

4 ± 4 (i simplified the answer).
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3


SECOND WAY:

9x^2 - 24x = 0

3x (3x - 8) = 0

3x = 0
3x-8 = 0

x = 0
x = 8/3