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How do you solve 6x22=x?

Answer
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Hint: Here given a algebraic equation firstly we have to convert the given equation to the quadratic equation ax2+bx+c=0 by shifting x from RHS to LHS. Later solve the quadratic equation by using the method of factorisation and find the factors and equate each factor to the zero to get the value of x.

Complete step by step solution:
Factorization means the process of creating a list of factors otherwise in mathematics, factorization or factoring is the decomposition of an object into a product of other objects, or factors, which when multiplied together give the original.

The general form of an equation is ax2+bx+c when the coefficient of x2 is unity. Every quadratic equation can be expressed as x2+bx+c=(x+d)(x+e). Here, b is the sum of d and e and c is the product of d and e.
Consider the given expression:
6x22=x
Subtract both side by x, then
6x22x=xx
On simplification, we get
6x2x2=0
The above equation similar like a quadratic equation ax2+bx+c now, solve by the method of factorization.
Now, Break the middle term as the summation of two numbers such that its product is equal to -12. Calculated above such two numbers are -4 and 3.
6x2+3x4x2=0
Making pairs of terms in the above expression
(6x2+3x)(4x+2)=0
Take out greatest common divisor GCD from the both pairs, then
3x(2x+1)2(2x+1)=0
Take (2x+1) common
(2x+1)(3x2)=0
Equate the each factor to zero, then
(2x+1)=0 or (3x2)=0
2x=1 3x=2
x=12 x=23

Hence, the required solution is x=12 or x=23.

Note: The equation is a quadratic equation. This problem can be solved by using the sum product rule. This defines as for the general quadratic equation ax2+bx+c, the product of ax2 and c is equal to the sum of bx of the equation. Hence we obtain the factors. The factors for the equation depend on the degree of the equation.
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