Question

How do you solve ${x^2} + 7x - 44 = 0$?

Answer 1

Hint: The given equation is a quadratic equation which will give two solutions after factorization.
In order to solve the given problem, we will use the method of splitting the middle term for factorization.
Factorization is the process of making factors of the given constant or polynomial having variables and constants.
Using the above hint we find out the factors of the given equation.

Complete step-by-step solution:
To factorize the above given quadratic equation we have two methods to solve one is the standard formula method and splitting the middle term, in this problem we will apply splitting the middle term method to factorize the quadratic equation.
Let’s discuss how to perform the splitting the middle term method.
For performing the factorization we have to find the two numbers which on addition or subtraction will give 7 and on multiplication the two numbers will give 44.
Pair of two numbers are; 11 and 4, 1 and 44 respectively.
Only 11 and 4 will give product as 44 and on subtracting 4 from 11 will give 7.
$ \Rightarrow {x^2} + 7x - 44 = 0$ (Given equation)
$ \Rightarrow {x^2} + 11x - 4x - 44 = 0$ (We have done the splitting of terms)
$ \Rightarrow x(x + 11) - 4(x + 11) = 0$ (Taken out common from the two brackets)
$ \Rightarrow (x - 4)(x + 11) = 0$ (The two brackets will be equated to zero)
$ \Rightarrow x = 4,x = - 11$ (Two values of x after factorization)

Therefore x is equal to 4 and -11.

Note: There is another method of making the factors of quadratic equation which is the standard one;
$\dfrac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}}$ , where a is the coefficient of x2, b is the coefficient of x and c is the constant term. The above formula gives the two factors as the formula contains two signs plus and minus.