Question

x²-6x+3=0 solve the equation by completing the square method

Answer 1

x^2 - 6x + 3 = 0

=> x^2 - 6x = - 3

=> x^2 - 6x + 3^2 = - 3 + 3^2

=> ( x - 3)^2 = - 3 +9

=> ( x - 3)^2 = 6

=> x - 3 = plus minus sqrt 6

=> x = 3 plus minus sqrt6

Alpha = 3 + sqrt6

Beta = 3 - sqrt6

Answer 2

Answer:

$x=3 \pm \sqrt{6}$

Step-by-step explanation:

Concept

• Completing the Square is a method used to solve a quadratic equation by changing the form of the equation so that the left side is a perfect square trinomial .

Find

Solve the equation by completing the square method

Solution

We have $(x-3)^{2}.$ This equals$x^{2}-6 x+9$

So we have the right $x^{2}$ and x terms, but not the right constant.

To make this equal the above equation, we need to subtract 6 and equate to 0 .

So:

$x^{2}-6 x+3=(x-3)^{2}-6=0$

We have completed the square.

We can then solve the equation

$(x-3)^{2}-6=0$

$(x-3)^{2}=6$

$x-3=\pm \sqrt{6}$

$x=3 \pm \sqrt{6}$

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