Question

n²-16=0
answer please​

Answer 1

Answer:

n^2 -16 = 0

n^2 = 16

n = √16

n = +4 , -4

Step-by-step explanation:

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Answer 2

changes made to your input should not affect the solution:

(1): "n2" was replaced by "n^2".

Step by step solution :

STEP

1

:

Trying to factor as a Difference of Squares

1.1 Factoring: n2-16

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 : 16 is the square of 4

Check : n2 is the square of n1

Factorization is : (n + 4) • (n - 4)

Equation at the end of step

1

:

(n + 4) • (n - 4) = 0

STEP

2

:

Theory - Roots of a product

2.1 A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation:

2.2 Solve : n+4 = 0

Subtract 4 from both sides of the equation :

n = -4

Solving a Single Variable Equation:

2.3 Solve : n-4 = 0

Add 4 to both sides of the equation :

n = 4

Two solutions were found :

n = 4

n = -4