Question

How do you factor the expression $6{{x}^{2}}+x=5$?

Answer 1

Hint: First we will convert the given equation into standard form. Then to solve the given equation we will use the split middle term method. In this method we will split the middle term of the equation $a{{x}^{2}}+bx+c=0$ such as the product of two numbers is equal to $a\times c$ and sum of two numbers is equal to $b$.

Complete step by step solution:
We have been given an equation $6{{x}^{2}}+x=5$.
We have to find the factors of the given equation.
First let us write the given equation into general form. Then we will get
$\Rightarrow 6{{x}^{2}}+x-5=0$
Now, we will use the split middle term method. We have to find two numbers such as the product of two numbers is equal to $a\times c=6\times 5=30$ and their sum is equal to $b=1$.
So we will use two numbers as 6 and 5.
So splitting the middle term we will get
$\Rightarrow 6{{x}^{2}}+\left( 6x-5x \right)-5=0$
Now, taking the common terms out we will get
$\Rightarrow 6x\left( x+1 \right)-5\left( x+1 \right)=0$
Now, again taking common factors out we will get
$\Rightarrow \left( 6x-5 \right)\left( x+1 \right)=0$
Hence we get the factors of the given equation as $\left( 6x-5 \right)\left( x+1 \right)$.

Note: Here in this question we use the split middle term method as it is a simple question. We can also use other methods like quadratic formula, completing the square method also to solve the equations. Also we can find the values of x by equating each factor to zero and by solving the obtained equations.