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21 October, 11:11

Solve the following equation for y.

2y + 2 = 36

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Answers (2)
  1. 21 October, 11:13
    0
    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
  2. 21 October, 11:40
    0
    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
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