Question 182105
(1)
 x^2 - x - 12= 0
(x - 4)(x + 3)= 0
x-4=0
x-4+4=0+4
x+0 = 4
x=4
****
x+3=0
x+3-3=0-3
x+0=-3
x=-3
answer:  x=4 or x=-3

(2)
x^2 + 8x + 15 =0
(x + 3)(x + 5)=0
x+3=0
x+3-3=0-3
x=-3
****
x+5=0
x+5-5=0-5
x=-5
answer: x=-3 or x=-5

(3)
LET
leg one=x
leg two=y
hypotenuse=h
x=9
h=y+3

Know: x^2 + y^2 = h^2
9^2 + y^2 = (y+3)^2
81 + y^2 = (y+3)(y+3)
81 + y^2 = y(y+3) + 3(y+3)
81 + y^2 = y(y) + y(3) + 3(y) + 3(3)
81 + y^2 = y^2 + 3y + 3y +9
81 + y^2 = y^2 + 6y + 9
81 + y^2 -y^2 = y^2 - y^2 + 6y + 9
81 + 0 = 0 + 6y + 9
81 -9 = 6y + 9 - 9
72 = 6y + 0
72/6 = 6y/6
12 = y

Then h=y+3 = 12+ 3 = 15

(4)
Ten more than the square of a number is seven times the number. Find all
x^2 + 10 = 7x
x^2 + 10 - 7x = 7x - 7x
x^2 + 10 - 7x =0
x^2 - 7x + 10 = 0
(x - 5)(x -2) = 0
x-5=0
x-5+5 = 0+5
x = 5
****
x-2=0
x-2+2=0+2
x=2
answer: x=5 or x=2