What is the first step in solving the equation x2 – 16/25 = 0?

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : 

                     x^2-(16/25)=0 

 2.1   Subtracting a fraction from a whole 

Rewrite the whole as a fraction using  25  as the denominator :

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole 

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

 2.2       Adding up the two equivalent fractions 
Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

 2.3      Factoring:  25x2 - 16 

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =
         A2 - AB + BA - B2 =
         A2 - AB + AB - B2 = 
         A2 - B2

Note :  AB = BA is the commutative property of multiplication. 

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check :  25  is the square of  5 
Check : 16 is the square of 4
Check :  x2  is the square of  x1 

Factorization is :       (5x + 4)  •  (5x - 4) 

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

Now, on the left hand side, the  25  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :
   (5x+4)  •  (5x-4)  = 0

 3.2    A product of several terms equals zero. 

 When a product of two or more terms equals zero, then at least one of the terms must be zero. 

 We shall now solve each term = 0 separately 

 In other words, we are going to solve as many equations as there are terms in the product 

 Any solution of term = 0 solves product = 0 as well.

 3.3      Solve  :    5x+4 = 0 

 Subtract  4  from both sides of the equation : 
                      5x = -4 
Divide both sides of the equation by 5:
                     x = -4/5 = -0.800 

 3.4      Solve  :    5x-4 = 0 

 Add  4  to both sides of the equation : 
                      5x = 4 
Divide both sides of the equation by 5:
                     x = 4/5 = 0.800 

4 puzzles in 3 hours

step-by-step explanation:

because linear equations are a lot simpler than quadratics equations, and linear equations formula is a lot easier to memorize. that's why i think they're harder.