Answer: x = 2 • ± √2 = ± 2.8284
Explanation:
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 : 8 is not a square !!
Ruling : Binomial can not be factored as the difference of two perfect squares.
Equation at the end of step 1 :
x2 - 8 = 0
Step 2 :
Solving a Single Variable Equation :
2.1 Solve : x2-8 = 0
Add 8 to both sides of the equation :
x2 = 8
When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:
x = ± √ 8
Can √ 8 be simplified ?
Yes! The prime factorization of 8 is
2•2•2
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).
√ 8 = √ 2•2•2 =
± 2 • √ 2
The equation has two real solutions
These solutions are x = 2 • ± √2 = ± 2.8284
Two solutions were found :
x = 2 • ± √2 = ± 2.8284
Not sure what you need help with, but I hope I helped you somehow.