If x^2+2=6x solve for x by completing the square.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The equation x^2 + 2 = 6x has to be solved by completion of squares.

x^2 + 2 = 6x

=> x^2 - 6x + 2 = 0

=> x^2 - 6x + 9 + 2 = 9

=> (x - 3)^2 = 7

=> x - 3 = `sqrt 7` and x - 3 = `-sqrt 7`

=> x = `3 + sqrt 7` and x = `3 - sqrt 7`

The roots of the equation are x = `3 + sqrt 7` and x = `3 - sqrt 7`

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atyourservice | Student, Grade 11 | (Level 3) Valedictorian

Posted on

`x^2+2=6x`

1. Get all the numbers on one side

`x^2-6x+2=0`

2.2 makes the problem not a perfect square so you need to minus 2

`x^2-6x=-2`

3. Now use the formula `(b / 2)^2`

`-6 / 2 = 3 = 3^2 = 9`

4.Plug in the 9, by adding it on both sides

`x^2-6x+9=7`

5. Now bring down the sqrt. of a and c, also the middle sign which is found between a and b

`(x-3)^2 = 7`

6. Find the square root 

`sqrt((x-3)^2) = sqrt(7)`

`x-3 = +-sqrt(7)`

`x=3+sqrt(7)`

`x= 3-sqrt(7)`

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