If 3x^2-2x+7=0,then (x-1/3)^2= with detailed steps because i dont really understand it. i know the answer is -20/9 but explain

Explanation:

A quadratic function is a kind of function with highest degree 2 .  Standard form of the quadratic equation : tex]ax^2+bx+c=0[/tex]

Further explanation:

Consider the given quadratic equation :  

First we divide both sides  by 3 , we get

--------(1)

Compare this equation to , we have

 [divide both sides by 2]

Now using the completing the squares method , Add and subtract to the left side in (1), we get

It can be written as

Use identity , we have

Subtract from both the sides , we get

Therefore, the value of

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Keywords :

Quadratic equation, standard form, completing squares method, Polynomial identities.

For this case we have the following polynomial:

To solve the problem, we must complete squares.

The first step is to divide the entire expression by 3.

We have then:

The second step is to place the constant term on the right side of the equation:

The third step is to complete the square:

Rewriting we have:

By completing squares we have:

the mistake in the pattern is that :

b. the decimal point was moved one too many place values each time

the correct pattern could be made by :

b. moving the decimal point to the right the same numbers of place values as the exponents