Question

Place the following steps in order to complete the square and solve the quadratic equation, x^2 - 6x + 7 = 0.

Answer 1

Answer:

$x^2-6x=-7$

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

$(x-3)^2=2$

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

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

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

Step-by-step explanation:

The given quadratic equation is

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

Subtract 7 from both sides.

$x^2-6x=-7$           ...(1)

If an expression is $x^2+bx$, then we add $(\frac{b}{2})^2$ to make it perfect square.

$(\frac{b}{2})^2=(\frac{-6}{2})^2=9$

Add 9 on both sides in equation (1).

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

$(x-3)^2=2$               $[\because (a-b)^2=a^2-2ab+b^2]$

Taking square root on both sides.

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

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

Add 3 on both sides.

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

Therefore, the correct order is F, A, D, C, E and B.

Answer 2

Answer:

option f

option a

option d

option c

option e

option b

Step-by-step explanation:

we have x^2 - 6x + 7 = 0

f) x^2 - 6x   = -7    

a) x^2 - 6x + 9 = -7+9

d) (x-3)^2=2

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

e) x-3=+-$\sqrt{2}$

b) x=3+-$\sqrt{2}$