Question

Place the following steps in order to complete the square and solve the quadratic equation x2-6x+7=0

Answer 1

Answer:

The solved expression is $x=3+\sqrt{2}$ and $x=3-\sqrt{2}$

Therefore $x=3\pm\sqrt{2}$

Step-by-step explanation:

Given quadratic equation is $x^2-6x+7=0$

To solve the given equation by using completing the square :

$x^2-6x+7=0$

Rewritting the above equation as below :

$x^2-6x+7+2-2=0$

$(x^2-6x+7+2)-2=0$

$(x^2-6x+9)-2=0$

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

$(x^2-2(x)(3)+3^2)-2=0$  ( it is of the form of $(a-b)^2=a^2-2ab+b^2$  heere a=x and b=3 )

$(x-3)^2-2=0$

$(x-3)^2=2$

Taking square root on both sides we get

$\sqrt{(x-3)^2}=\pm\sqrt{2}$

$x-3=\pm\sqrt{2}$

$x=\pm\sqrt{2}+3$

$x=3\pm\sqrt{2}$

Therefore $x=3+\sqrt{2}$ and $x=3-\sqrt{2}$