[quadratic equations 2][section 65]
(1.) y2 - 4 = 0 here is the problem
+4 +4
add 4 to each side
_______________
y2 = 4 add
y = 2 y = -2
take square roots
result: y = 2, y = -2
(2.) x2 - 11 = 0 here is the problem
+ 11 +11
add 11 to each side
______________
x2 = 11 add
__
__
x = √11 x = -√11 take square roots
__ __
results: x = √11 x = -√11
(3.) 2r2 = 200 here is the problem
__
____
2 2 divide each side by 2
r2 = 100 divide
r = 10 r = -10
take square roots
results: x = 10 , r
= -10
(4.) 3(a + 6)2 = 27 here is the problem
_________ ___
3 3 divide each side by 3
(a + 6)2 = 9 divide
a + 6 = 3 a + 6 = -3 take square roots
-
6 -6 - 6
-6 subtract 6 from each side
________________ ________________
a = -3 , a
= -9 subtract
results: a = -3, a = -9
(5.) (x + 7)2 = 49 here is the problem
x + 7 = 7 x + 7 = -7 take square roots
-7 -7
-7 -7 subtract 7 from each side
____________ _______________
x = 0 , x
= -14 subtract
results: x = 0 , x =
-14
(6.) 5(b - 2)2 = 125 here is the problem
__________ _______
5 5 divide each side by 5
(b - 2)2 = 25 divide
b - 2 = 5 b - 2 = -5 take square roots
+
2 +2 +2
+2 add 2 to each side
_____________ ________________
b = 7
, b = -3 add
results: x = 7 , b =
-3
(7.) (x + 17)2 = 49 here is the problem
x + 17 = 7 x + 17 = -7 take square roots
-17 -17
-17 -17 subt 17 fr ea side
________________ ________________
x = -10
, x = -24 subtract
results: x = -10 , x = -24
(8.) (x + 5)2 = 16 here is the problem
x + 5 = 4 x + 5 = -4 take square roots
- 5 -5
-5 -5 subtract 5 from each side
______________ _______________
x = -1 ,
x = -9 subtract
results: x = -1 , x =
-9
(9.) 10(3a + 7)2 = 1000 here is the problem
____________ _________
10 10 divide each side by 10
(3a + 7)2 = 100 divide
3a + 7 = 10 3a + 7 = -10 take square roots
-7 -7
-7 -7 subt 7 from each side
_______________ _______________
3a
= 3 ,
3a = -17
subtract
___ ___
_____ _____
3 3 3
3 divide each side by 3
a = 1 , a
= -5 2/3 divide
results: a = 1 , a =
-5 2/3
(10.) 4(3x - 2)2 = 36 here is the problem
_________ ____
4 4 divide each side by 4
(3x - 2)2 = 9 divide
3x - 2 = 3 3x - 2 = -3 take square roots
+
2 + 2 +2
+2 add 2 to each side
_______________ _________________
3x = 5 ,
3x = -1 add
__
__ __ ____
3
3 3 3
divide each side by 3
x = 5/3 x = -1/3 cancel
results: x = 5/3 , x = -1/3