Solve the following equation for y.

2y + 2 = 36

y = 3 • ± √2 = ± 4.2426

Step-by-step 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

Solving step by step:

2y + 2 = 36

Move the constant to the right and change the sign.

2y = 36 - 2

Calculate the right side.

2y = 34

Divide both sides by 2.

y = 17