Question

Solve the equation x^2 - 4x + 6 = 9 by completing the square.

Answer 1

Hello!

x² - 4x + 6 = 9 <=>

<=> x² - 4x + 6 - 9 = 0 <=>

<=> x² - 4x - 3 = 0 <=>

<=> x = -(-4)±√(-4)²-4×1×(-3)/2×1 <=>

<=> x = 4±√16+12/2 <=>

<=> x = 4±√28/2 <=>

<=> x = 4±2√7/2 =>

=> x = 4+2√7/2 and x = 4-2√7/2 =>

=> x = 2+√7 and x = 2-√7

The equation has two solutions.

Good luck! :)

Answer 2

Answer:  $x= 2 + \sqrt{7}\\ or \\ x= 2 - \sqrt{7}$

how i got it?

$x^2 - 4x + 6 = 9$

*subtract 9 on both sides*

$x^2 - 4x + 6 - 9 = 0$  ( which turns to) $x^2 - 4x - 3=0$

a=1 or x, b=-4, c=-3

Step 2: Use quadratic formula with a=1, b=-4, c=-3.

$x= - (-4) + or - \sqrt{-4}x^{2} -4(1)(-3) / 2(1)$

which turns to: x= 4 + or - √28 divided by 2

the final answer should be $x= 2 + \sqrt{7}\\ or \\ x= 2 - \sqrt{7}$