Question

slve quadratic equation by factoring
1. x²-5x=0
2. (x+4) (x-3)=0
3. x²+5x+4=0
4.x²-7x= -12
5. 2x²-x-6=0​

Answer 1

2.(x+4)(x+3)=0

Therefore,x+4=0 or x+3=0

or,x=-4 or x=-3

3.x²+5x+4=0

or,x²+(1+4)x+4=0

or,x²+x+4x+4=0

or,x(x+1)+4(x+1)=0

or,(x+4)(x+1)=0

Therefore, x+4=0 or x+1=0

or, x=-4 or x=-1

4.x²-7x=-12

or,x²-7x+12=0

or,x²-(3+4)x+12=0

or x²-3x-4x+12=0

or,x(x-3)-4(x-3)

or,(x-4)(x-3)=0

or,x=3 or x=4

Answer 2

Answer:

(1) x^2-5x=0

x(x-5)=0

either, or, x-5=0

x=0. x=5

(2) (x+4)(x-3)=0

either, x+4=0. or, x-3=0

x=-4 x=3

(3) x^2+5x+4=0

x^2+(4+1)x+4=0

x^2+4x+x+4=0

x(x+4)+1(x+4)=0

(x+4)(x+1)=0

either, x+4=0. or, x+1=0

x=-4 x=-1

(4) x^2-7x=-12

x^2-7x+12=0

x^2-(4+3)x+12=0

x^2-4x-3x+12=0

x(x-4)-3(x-4)=0

(x-4)(x-3)=0

either, x-4=0. or, x-3=0

x=4. x=3

(5) 2x^2-x-6=0

2x^2-(4-3)x-6=0

2x^2-4x+3x-6=0

2x(x-2)+3(x-2)=0

(x-2)(2x+3)=0

either, x-2=0. or, 2x+3=0

x=2. 2x=-3

x=-3/2