Question

How to solve this equation x²=16​

Answer 1

There are two I results found which is x=4 and x=-4

Explanation:

Step by Step Solution:

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Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

x^2-(16)=0

Step by step solution :

STEP

1 :

Trying to factor as a Difference of Squares:

1.1 Factoring: x2-16

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 : x2 is the square of x1

Factorization is : (x + 4) • (x - 4)

Equation at the end of step

1 :

(x + 4) • (x - 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 : x+4 = 0

Subtract 4 from both sides of the equation :

x = -4

Solving a Single Variable Equation:

2.3 Solve : x-4 = 0

Add 4 to both sides of the equation :

x = 4 and/or x=-4

Answer 2

Explanation:

Hey there!

To solve this type of question, you must take square of variable"X" to right side making it ±squareroot. As it is a quadratic equation it will have two values (±).

Given;

`{x}^(2) = 16`

Taking (square) to right side. It becomes ± square root.

`x = + - √(16)`

`x = + - \sqrt{ {4}^(2) }`

Cancel square and square root.

`x = + - 4`

Therefore, X = ±4

Hope it helps...