[quadratic equations][section 47]
(1.) x2 - 5x - 6 = 0 here is the problem
(x - 6)(x + 1) = 0 factor
x - 6 = 0 x + 1 = 0
set each factor equal to 0
+ 6 +6
-1 -1 add this to each side
____________ __________
x = 6 ,
x = -1 add
result: x = 6, x = -1
(2.) x2 - 5x + 6 = 0 here is the problem
(x - 2)(x - 3) = 0 factor
x - 2 = 0 x - 3 = 0 set each factor equal to 0
+ 2
+2 + 3
+3 add this to each side
_________ ______________
x = 2
, x = 3 add
result: x = 2 , x =
3
(3.) x2 - 3x - 10 = 0 here is the problem
(x - 5)(x + 2) = 0 factors
x - 5 = 0 x + 2 = 0
set each factor equal to 0
+ 5
+5 - 2 -2
add this to each side
_________ ___________
x
= 5 , x =
-2 add
result: x = 5 , x =
-2
(4.) n2 + n = 0 here is the problem
n(n + 1) = 0 factor
n = 0
n + 1 = 0 set each factor equal
to 0
-1 -1
subtract 1 from each side
________ _____________
n =
0 ,
n = -1 subtract
result: n = 1 , x = -1
(5.) y2 + 7y = 0 here is the problem
y(y + 7) = 0 factor
y = 0 y + 7 = 0 set each factor equal to 0
-7 -7
subtract 7 from each side
__________ ___________
y = 0 , y
= -7 subtract
result: y = 0 , y = -7
(6.) c2 - 49 = 0 here is the problem
(c - 7)(c + 7) = 0 factor
c - 7 = 0 c + 7 = 0
set each factor equal to 0
+
7 + 7 - 7 -7
add this to each side
___________ _____________
c = 7 , c
= -7 add
(7.) 3x2 - 2 = x2
+ 6 here is the problem
+ 2
+ 2 add 2 to each side
_____________________
3x2 = x2
+ 8 add
-x2 -x2 subtract x2 from each side
__________________
2x2 =
8 subtract
____ _____
2 2 divide each side by 2
x2 = 4 divide and cancel
-4 -4
subtract 4 from each side
_______________
x2 - 4 = 0 subtract
(x - 2)(x + 2) = 0 factor
x - 2 = 0 x + 2 = 0 set each factor equal to 0
+ 2 +2 -
2 -2 add this to each side
_______________ ______________
x = 2 ,
x = -2 add
result: x = 2 , x =
-2
(8.) 23p - 6 = -4p2 here is the problem
+4p2 + 4p2 add 4p2 to each side
_____________________
4p2 + 23p - 6 = 0 add
(4p - 1)(p + 6) = 0 factor
4p - 1 = 0 p + 6 = 0
set each factor equal to 0
+
1 +1 - 6 -6
add this to each side
____________ _____________
4p
= 1 , p
= -6 add
___ __
4 4
divide each side by 4
p = 1/4 , p
= -6
result: p = 1/4 , p
= -6
(9.) p3 - 13p2 +
36p = 0 here is the problem
p(p2 - 13p + 36) = 0 factor
p(p - 4)(p - 9) = 0 factor
p = 0 p - 4 = 0 p - 9 = 0
set each factor equal to 0
+4 +4
+ 9 +9
add this to each side
____
__________ _________
p = 0 ,
p = 4 , p = 9
add
result: p = 0 , p = 4, p = 9
(10.) y3 - 16y2 =
0 here is the problem
y2(y - 16) = 0 factor
y = 0
y - 16 = 0 set each factor
equal to 0
+ 16 +16 add 16 to each side
_________ _______________
y = 0
, y = 16 add
result: y = 0 , y = 16