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
Step by step solution :Step 1 : 16
Simplify ——
25
Equation at the end of step 1 : 16
(x2) - —— = 0
25
Step 2 :Rewriting the whole as an Equivalent Fraction :
2.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using 25 as the denominator :
x2 x2 • 25
x2 = —— = ———————
1 25
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
Adding fractions that have a common 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:
x2 • 25 - (16) 25x2 - 16
—————————————— = —————————
25 25
Trying to factor as a Difference of Squares :
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)
Equation at the end of step 2 : (5x + 4) • (5x - 4)
——————————————————— = 0
25
Step 3 :When a fraction equals zero : 3.1 When a fraction equals zero ...
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:
(5x+4)•(5x-4)
————————————— • 25 = 0 • 25
25
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
Theory - Roots of a product :
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.
Solving a Single Variable Equation :
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
Solving a Single Variable Equation :
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
x = 4/5 = 0.800
x = -4/5 = -0.800
