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 :<span>Step 1 :</span> 16
Simplify ——
25
<span>Equation at the end of step 1 :</span><span><span> 16
(x2) - —— = 0
25
</span><span> Step 2 :</span></span>Rewriting the whole as an Equivalent Fraction :
<span> 2.1 </span> Subtracting a fraction from a whole
Rewrite the whole as a fraction using <span> 25 </span> as the denominator :
<span> x2 x2 • 25
x2 = —— = ———————
1 25
</span>
<span>Equivalent fraction : </span>The fraction thus generated looks different but has the same value as the whole
<span>Common denominator : </span>The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
<span> 2.2 </span> 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:
<span> x2 • 25 - (16) 25x2 - 16
—————————————— = —————————
25 25
</span>Trying to factor as a Difference of Squares :
<span> 2.3 </span> Factoring: <span> 25x2 - 16</span>
Theory : A difference of two perfect squares, <span> A2 - B2 </span>can be factored into <span> (A+B) • (A-B)
</span>Proof :<span> (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 <span>- AB + AB </span>- B2 =
<span> A2 - B2</span>
</span>Note : <span> <span>AB = BA </span></span>is the commutative property of multiplication.
Note : <span> <span>- AB + AB </span></span>equals zero and is therefore eliminated from the expression.
Check : 25 is the square of 5
Check : 16 is the square of 4
Check : <span> x2 </span>is the square of <span> x1 </span>
Factorization is : (5x + 4) • (5x - 4)
<span>Equation at the end of step 2 :</span> (5x + 4) • (5x - 4)
——————————————————— = 0
25
<span>Step 3 :</span>When a fraction equals zero :<span><span> 3.1 </span> When a fraction equals zero ...</span>
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the <span>denominator, </span>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 <span> 25 </span> 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 :
<span> 3.2 </span> A product of several terms equals zero.<span>
</span>When a product of two or more terms equals zero, then at least one of the terms must be zero.<span>
</span>We shall now solve each term = 0 separately<span>
</span>In other words, we are going to solve as many equations as there are terms in the product<span>
</span>Any solution of term = 0 solves product = 0 as well.
Solving a Single Variable Equation :
<span> 3.3 </span> Solve : 5x+4 = 0<span>
</span>Subtract 4 from both sides of the equation :<span>
</span> 5x = -4
Divide both sides of the equation by 5:
x = -4/5 = -0.800
Solving a Single Variable Equation :
<span> 3.4 </span> Solve : 5x-4 = 0<span>
</span>Add 4 to both sides of the equation :<span>
</span> 5x = 4
Divide both sides of the equation by 5:
x = 4/5 = 0.800
<span><span> x = 4/5 = 0.800
</span><span> x = -4/5 = -0.800
</span></span>
