Question

Solve the given equation ${x^2} - 36 = 0$?

Answer 1

For solving the quadratic equation you can use factorization method in order to obtain the solution of the variable which is asked in the question. While factoring you have to see the mid term splitting rule or if the question can be formed in any algebraic identity then you can directly compare and solve the question.

Formulae Used: ${a^2} - {b^2} = (a + b)(a - b)$

Complete step by step solution:
For the given question ${x^2} - 36 = 0$:

Algebraic identity ${a^2} - {b^2} = (a + b)(a - b)$ can be used and easy factors and values of variables can be obtained.

By simplifying the equation and making in the form of the above identity we get;

$${x^2} - 36 = 0 \\\ {x^2} - {(6)^2} = 0 \\\ comparing\,with\,{a^2} - {b^2}\,we\,get; \\\ a = x,\,b = 6 \\\$$

Now after getting the values according to the algebraic identity the solution can be written as :

$${x^2} - 36 = 0 \\\ (x + 6)(x - 6) = 0 \\\ x = - 6,\,6 \\\$$

On equating each bracket equals to zero we obtained the values for the given variable “x”

Now here no restriction is given for the values of the variable hence both the values of “x” are acceptable and is the final solution.

Additional Information: In order to compare the given equation with the standard equation you have to write the equation exactly as written for the general algebraic identity.

Note: For such an equation you have to compare with the standard equation, for that you need to compare First the “a”,”b” and accordingly you can go with the adjustment needed for exact comparison. Something few comparisons are needed with “a” also but mostly the constant term is needed to be edited after adding or subtracting some quantity on both sides of the equation.