Answer:
y = 3 • ± √2 = ± 4.2426
Explanation:
2y2 - 36 = 0
Step 2 :
Step 3 :
Pulling out like terms :
3.1 Pull out like factors :
2y2 - 36 = 2 • (y2 - 18)
Trying to factor as a Difference of Squares :
3.2 Factoring: y2 - 18
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 : 18 is not a square !!
Ruling : Binomial can not be factored as the difference of two perfect squares.
Equation at the end of step 3 :
2 • (y2 - 18) = 0
Step 4 :
Equations which are never true :
4.1 Solve : 2 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solving a Single Variable Equation :
4.2 Solve : y2-18 = 0
Add 18 to both sides of the equation :
y2 = 18
When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:
y = ± √ 18
Can √ 18 be simplified ?
Yes! The prime factorization of 18 is
2•3•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).
√ 18 = √ 2•3•3 =
± 3 • √ 2
The equation has two real solutions
These solutions are y = 3 • ± √2 = ± 4.2426