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: [tex]x= 2 + \sqrt{7}\\ or \\ x= 2 - \sqrt{7}[/tex]
how i got it?
[tex]x^2 - 4x + 6 = 9[/tex]
*subtract 9 on both sides*
[tex]x^2 - 4x + 6 - 9 = 0[/tex] ( which turns to) [tex]x^2 - 4x - 3=0[/tex]
a=1 or x, b=-4, c=-3
Step 2: Use quadratic formula with a=1, b=-4, c=-3.
[tex]x= - (-4) + or - \sqrt{-4}x^{2} -4(1)(-3) / 2(1)[/tex]
which turns to: x= 4 + or - √28 divided by 2
the final answer should be [tex]x= 2 + \sqrt{7}\\ or \\ x= 2 - \sqrt{7}[/tex]
