Question

x²- 36=?.............​

Answer 1

Step-by-step explanation:

Changes made to your input should not affect the solution:

(1): "x2" was replaced by "x^2".

Rearrange:

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

x^2-(36)=0

Step by step solution :

STEP

1

:

Trying to factor as a Difference of Squares

1.1 Factoring: x2-36

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 : 36 is the square of 6

Check : x2 is the square of x1

Factorization is : (x + 6) • (x - 6)

Equation at the end of step

1

:

(x + 6) • (x - 6) = 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+6 = 0

Subtract 6 from both sides of the equation :

x = -6

Solving a Single Variable Equation:

2.3 Solve : x-6 = 0

Add 6 to both sides of the equation :

x = 6

Two solutions were found :

x = 6

x = -6

Answer 2

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$\sf \: {x}^{2} = 36 \\ \implies \sf \: {x} = \sqrt{36} \\ \implies \sf \: \fbox{ \sf \: x = 6 or (-6)}$