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Solve for$x:$ $6{x^2} + 5x - 1 = 0$

Last updated date: 24th Mar 2023
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Hint:Factorization is exactly opposite of multiplication. In multiplication we multiply two or more terms or numbers to get one term or number. The Process of writing an algebraic expression as a product of two or more expressions is called factorization.

Complete step by step answer:
In this type of factorization we need to take common factors of a given expression and then we need to simplify and write it again. So, the equation is,
$6{x^2} + 5x - 1 = 0$
$\Rightarrow 6{x^2} + 6x - x - 1 = 0 \\
\Rightarrow 6x(x + 1) - 1(x + 1) = 0 \\
\Rightarrow (x + 1)(6x - 1) = 0 \\
\Rightarrow x = - 1,6x = 1 \\
\therefore x = - 1,x = \dfrac{1}{6}$

Hence, the values of $x$ are - 1 and $\dfrac{1}{6}$.

Note:There is another way of factorization by grouping, in this type of factorization we need to arrange the terms of the given expression in such a way that we can take common factors in each group. These are the numbers when multiplied give another number. In other words, pairs of all the numbers whose product results in one single number are said to be the factors of that number.