Answer: 1. x=-0.5, x=3 2. x=2/3, x=1 3. x=-7, x=3 4. x=6 5. x=0, x=18
Step-by-step explanation:
1. 2x²-5x-3=0
(2x+1)(x-3)=0
2x+1=0, x-3=0
2x+1=0, x-3=0
2x=-1 x=3
x=-1/2
The roots are -0.5 and 3
2. 3x²+x-2 =0
(3x-2)(x+1)=0
3x=2 x=-1
The roots are 2/3 and -1
3. x²+4x-21=0
(x+7)(x-3)=0 because 7×-3 is -21 and 7-3 is 4
x+7=0, x-3=0
x=-7 x=3
The roots are -7 and 3
4. This is not a quadratic equation so it cannot be factored
x²-12=24
x²=24+12
x²=36
x=6
5. x²-18x=0
(x-18)(x)=0
x-18=0, x=0
x=18
Double check the answers yourself in case I made a mistake.