Question

Solve 2x² = 324 using the square root property.

Answer 1

Step-by-step explanation:

STEP

1

:

Equation at the end of step 1

2x2 - 324 = 0

STEP

2

:

STEP

3

:

Pulling out like terms

3.1 Pull out like factors :

2x2 - 324 = 2 • (x2 - 162)

Trying to factor as a Difference of Squares:

3.2 Factoring: x2 - 162

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 : 162 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 • (x2 - 162) = 0

STEP

4

:

Equations which are never true

hope it helps