Question

Find all possible value of the given variable 

1.h²+5h=0
2.z²-z=0
3.m²+13m+40=0
4.z²-3z=0
5.q²+7q=0
6.k²+2k=0
7.x²-3x-70=0
8.q²+7q-60=0
9.z²+9z-36=0
10.d²-13d+22=0

Answer 1

`1.\\ \\ h^2+5h=0 \\ \\h(x+5)=0\\ \\x=0 \ \ \ or \ \ \ x+5 =0\ \ |-5\\ \\x+5-5=0-5\\ \\x=0 \ \ \ or \ \ \ x=-5`



`2.\\ \\ z^2-z=0\\ \\z(x-1)=0\\ \\z=0 \ \ \ or \ \ \ z-1 =0 \ \ | +1\\ \\z-1+1 =0 +1 \\ \\x=0 \ \ \ or \ \ \ z=1`



`3.\\ \\m^2+13m+40=0 \\ \\a=1 ,\ b=13, \ c=40 \\ \\\Delta =b^2-4ac =13^2-4\cdot 1\cdot 40=169 - 1600=-1431 \\ \\and \ we \ know \ when \ \Delta \ is \ negative, \ theres \ no \solution`



`4.\\ \\z^2-3z=0 \\ \\ (z-3)=0\\ \\z=0 \ \ \ or \ \ \ z-3 =0\ \ |+3\\ \\ z-3+3=0+3\\ \\z=0 \ \ \ or \ \ \ z=3`



`5.\\ \\q^2+7q=0 \\ \\q(q+7)=0\\ \\q=0 \ \ \ or \ \ \ q+7 =0\ \ |-7\\ \\q+7-7=0-7\\ \\q=0 \ \ \ or \ \ \ q=-7`



`6.\\ \\k^2+2k=0\\ \\k(k+2)=0\\ \\k=0 \ \ \ or \ \ \ k+2 =0\ \ |-2\\ \\k+2-2=0-2\\ \\k=0 \ \ \ or \ \ \ k=-2`



`7. \\ \\ x^2-3x-70=0 \\ \\a=1,\ b=-3, \ c=-70 \\ \\\Delta =b^2-4ac = (-3)^2-4\cdot 1\cdot (-70)= 9+280=289\\ \\ x_(1)=(-b-√(\Delta) )/(2a)=(3-√(289))/(2 )=( 3-17)/(2)=(-14)/(2)=-7`


`x_(2)=(-b+√(\Delta) )/(2a)=(3+√(289))/(2 )=( 3+17)/(2)=(20)/(2)=10\\ \\(x+7)(x-10)=0`



`8.\\ \\q^2+7q-60=0 \\ \\a=1,\ b=7, \ q=-60 \\ \\\Delta =b^2-4ac = 7^2-4\cdot 1\cdot (-60)=49+240=289 \\ \\ x_(1)=(-b-√(\Delta) )/(2a)=(-7-√(289))/(2 )=( -7-17)/(2)=(-24)/(2)=-12`


`x_(2)=(-b+√(\Delta) )/(2a)=(-7+√(289))/(2 )=( -7+17)/(2)=( 10)/(2)= 5\\ \\(x+12)(x-5)=0`



`9.\\ \\z^2+9z-36=0 \\ \\a=1,\ b=9, \ q=-36 \\ \\\Delta =b^2-4ac = 9^2-4\cdot 1\cdot (-36)= 81+144=225\\ \\ x_(1)=(-b-√(\Delta) )/(2a)=(-9-√(225))/(2 )=( -9-15)/(2)=(-24)/(2)=-12`


`x_(2)=(-b+√(\Delta) )/(2a)=(-9+√(225))/(2 )=( -9+15)/(2)=(6)/(2)=3\\ \\(x+11)(x-3)=0`



`10.\\ \\d^2-13d+22=0 \\ \\a=1,\ b=-13, \ q=22 \\ \\\Delta =b^2-4ac = (-13)^2-4\cdot 1\cdot 22= 169-88=81\\ \\ d_(1)=(-b-√(\Delta) )/(2a)=(13-√(81))/(2 )=( 13-9)/(2)=(4)/(2)=2`


`d_(2)=(-b+√(\Delta) )/(2a)=(13+√(81))/(2 )=( 13+9)/(2)=(22)/(2)=11\\ \\(d-2)(d-11)=0`