Answer:
Step-by-step explanation:
Trying to factor as a Difference of Squares :
1.1 Factoring: r2-96
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 : 96 is not a square !!
Ruling : Binomial can not be factored as the difference of two perfect squares.
Equation at the end of step 1 :
r2 - 96 = 0
Step 2 :
Solving a Single Variable Equation :
2.1 Solve : r2-96 = 0
Add 96 to both sides of the equation :
r2 = 96
When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:
r = ± √ 96
Can √ 96 be simplified ?
Yes! The prime factorization of 96 is
2•2•2•2•2•3
To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).
√ 96 = √ 2•2•2•2•2•3 =2•2•√ 6 =
± 4 • √ 6
The equation has two real solutions
These solutions are r = 4 • ± √6 = ± 9.7980
Two solutions were found :
r = 4 • ± √6 = ± 9.7980
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