1.) 81 - 4x² =0 and this ,,, 2.) x² -25=0 ?

Question

can anyone please explain this to me? ...

Answer 1

1)

 

0.81 - 4x² = 0

 

0.81 is equivalent to 81/100.

 

 

(81/100) - 4x² = 0

 

 

81/100 is a perfect square and 4x² is a perfect square.  Since we have subtraction, this is a difference of perfect squares.

 

(9/10 - 2x)(9/10 + 2x) = 0

 

 

Set the factors equal to zero.

 

(9/10) - 2x = 0                 and              (9/10) + 2x = 0

 

-2x = -9/10                      and                 2x = -9/10

 

x = (-1/2)(-9/10)              and                  x = (1/2)(-9/10)

 

x = 9/20                           and                 x = -9/20

 

 

Knowing this, try the next one on your own.

Answer 2

81-4x²=0

 

note the formula for the difference of two squares.

a²-b²=(a-b)(a+b)

81-4x²= (9²)-(2x)² so a=9, b=2x

 

81-4x²= (9-2x)(9+2x)=0

 

setting that equal to zero we have

9-2x= 0     or     9+2x=0

9=2x                 9=-2x

x=9/2        or     x=-9/2

 

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x²-25=0

Again we have difference of two squares

x²-5²=(x-5)(x+5)=0

 

either x-5=0   or  x+5=0

x=5 or x=-5