Answer:

1. 2x²-3x+7=0 ( the values of a=2, b=-3, c=7)

2. 2x²+6x-5=0 ( the values of a=2, b=6, c=-5)

3. x²+7x+12=0 ( the values of a=1, b=7, c=12)

4. 2x²+5x-7=0 ( the values of a=2, b=5, c=-7)

5. 2x²-6x-15=0 ( the values of a=2, b=-6, c=-15)

6. x²+3x-49=0 ( the values of a=1, b=3, c=-49)

7. x²-8x+24=0 ( the values of a=1, b=-8, c=24)

8. x²+x-2=0 ( the values of a=1, b=1, c=-2)

9. 2x²-6x=0 ( the values of a=2, b=-6, c=0)

10. x²+14x-9=0 ( the values of a=1, b=14, c=-9)

Step-by-step explanation:

1. 3x-2x²=7 (ax²+bx+c=0 arrange using standard form)

-2x²+3x-7=0 ( note, if the constant in the right side is + it will become - if you transfer in the left side,vice versa if - it will become +)

(-2x²+3x-7=0)-1 [also the rule in standard form is ""A cannot be negative ""(-) so we should multiply it by -1 )] remember that if you multiply (-)(-) the answer is positive.

answer:

2x²-3x+7=0 ( the values of a=2, b=-3, c=7)

2. 5-2x²=6x (arrange same method in #1)

-2x²+5=6x

-2x²-6x+5=0

(-2x²-6x+5=0)-1

answer:

2x²+6x-5=0 ( the values of a=2, b=6, c=-5)

3.(x+3)(x+4)=0 (use the foil or smile method)

x²+4x+3x+12=0

answer:

x²+7x+12=0 ( the values of a=1, b=7, c=12)

4. (2x+7)(x-1)=0 [same method in #3]

2x²-2x+7x-7=0

answer:

2x²+5x-7=0 ( the values of a=2, b=5, c=-7)

5. 2x(x-3)=15

2x²-6x=15

answer:

2x²-6x-15=0 ( the values of a=2, b=-6, c=-15)

6. (x+7)(x-7)=-3x 0 [same method in #3]

x²-7x+7x-49=-3x

x²-49+3x=0 (arrange)

answer:

x²+3x-49=0 ( the values of a=1, b=3, c=-49)

7. (x-4)²+8=0

( x-4)( x-4)+8=0

x²-4x-4x+16+8=0

answer:

x²-8x+24=0 ( the values of a=1, b=-8, c=24)

8. (x+2)²=3(x+2) [same method in # 3]

x²+2x+2x+4=3x+6

x²+4x+4-3x-6=0

answer:

x²+x-2=0 ( the values of a=1, b=1, c=-2)

9. (2x-1)²=(x+1)² [same method in # 3]

(2x-1)(2x-1)=(x+1)(x+1)

4x²-4x+1= 2x²+2x+1

4x²-4x+1-2x²-2x-1=0

answer:

2x²-6x=0 ( the values of a=2, b=-6, c=0)

10. 2x(x+4)=(x-3)(x-3)

2x²+8x=x²-6x+9

2x²+8x-x²+6x-9=0

answer:

x²+14x-9=0 (the values of a=1, b=14, c=-9)