Question

Joseph has started completing the square on the equation 3x2 - 7x + 12 = 0. He has worked to the point where he has the expression x2 - 7/4x = -4. Use complete sentences describe Joseph’s steps up to this point and whether or not his work is accurate.

Answer 1

3x^2 - 7x + 12 = 0 ....subtract 12 from both sides
3x^2 - 7x = -12 ....divide both sides by 3 to get x^2 by itself
x^2 - 7/3x = -4

His work is not accurate because he divided the second term by 4 instead of 3.

Answer 2

His work is not accurate.

Explanation:

Since, when we solve a quadratic equation by completing the square method,

Then, we follow the following steps,

Step 1 : Move the constant term to the right side of the equation,

Step 2 : Make 1 as the coefficient of
`x^2`

Step 3 : Add the square of the half of the coefficient of the x in both sides.

Here, the given equation is,

`3x^2-7x+12=0`

Step 1 :
`3x^2-7x=-12`

Step 2 :
`x^2-(7)/(3)x=-4`

Since, in the Joseph's work the above expression is
`x^2-(7)/(4)x=-4`

Hence, his work is not accurate because he divide the second term of the left side of equation by 4 instead of 3.