[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