How do you solve these problems by using the
quadratic formula x² = 6x - 4 and
x² + 16x + 60 = 5
x² = 6x - 4
Get 0 on the right by adding -6x + 4 to both sides
x² - 6x + 4 = 0
Use the quadratic formula:
______
-b ± Öb²-4ac
x = —————————————
2a
where a = 1; b = -6; c = 4
_____________
-(-6) ± Ö(-6)²-4(1)(4)
x = ————————————————————————
2(1)
_____
6 ± Ö36-16
x = ————————————
2
__
6 ± Ö20
x = —————————
2
___
6 ± Ö4·5
x = ——————————
2
_
6 ± 2Ö5
x = —————————
2
_
6 2Ö5
x = ——— ± —————
2 2
_
x = 3 ± Ö5
_
Using the +, x = 3 + Ö5, which
is one solution and equals about 5.236067977
_
Using the -, x = 3 - Ö5, which
is the other solution and equals about
.583592135
==============================
x² + 16x + 60 = 5
Get 0 on the right by adding -5 to both sides
x² + 16x + 55 = 0
Use the quadratic formula:
______
-b ± Öb²-4ac
x = —————————————
2a
where a = 1; b = 16; c = 55
______________
-(16) ± Ö(16)²-4(1)(55)
x = ——————————————————————————
2(1)
_______
-16 ± Ö256-220
x = ————————————————
2
__
-16 ± Ö36
x = —————————————
2
-16 ± 6
x = —————————
2
-16 6
x = ———— ± ———
2 2
x = -8 ± 3
Using the +, x = -8 + 3, which
is one solution and equals -5
Using the -, x = -8 - 3, which
is the other solution and equals -11
Edwin
