solve for x: 2x^2-4x-6=0?

2x^2 - 4x - 6 = 0

multiply the first and last numbers together:

2 * -6 = -12

find 2 numbers that multiply to -12 and add to the middle number (which is -4)

-6 * 2 = -12

-6 + 2 = -4

rewrite the equation using 2 and -6

2x^2 + 2x - 6x - 6 = 0 ***notice this is the SAME as the original)***

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

factor these into:

2x(x + 1) - 6(x + 1)

***notice there are two (x + 1)'s!!!***

take whatever is outside the parenthesis and put them in parenthesis.

(2x - 6)(x + 1) = 0

simple as that!

2x - 6 = 0
2x = 6
x = 3

x + 1 = 0
x = -1

x = 3 and -1




same deal with the second problem. i wont write every step but i'll solve it the same way.

3x^2 + 7x + 2 + 0

3x^2 + 7x + 2 = 0

6 * 1 = 6
6 + 1 = 7

3x^2 + 6x + 1x + 2 = 0

(3x^2 + 6x) + (1x + 2)

3x(x + 2) + 1(x + 2)

(3x + 1)(x + 2) = 0

3x + 1 = 0
3x = -1
x = -1/3

x + 2 = 0
x = -2

x = -1/2 and -2


i hope this helped!

4x 6 2

at the start im assuming its 2*2 + 4x = 6 so 4+4x = 6 then we subtract the 4 over to the different area so we've: 4x = 2 then we divide 4 on the two sides so we've: x = 2/4 = a million/2

1)
2x^2 - 4x - 6 = 0
(2x^2 - 4x - 6)/2 = 0/2
x^2 - 2x - 3 = 0
(x + 1)(x - 3) = 0

x + 1 = 0
x = -1

x - 3 = 0
x = 3

∴ x = -1 , 3

= = = = = = = =

2)
3x^2 + 7x + 2 = 0
(3x + 1)(x + 2) = 0

3x + 1 = 0
3x = -1
x = -1/3

x + 2 = 0
x = -2

x = -1/3 , -2

x= -1 and +3
x= -1/3 and -2

That is a quadratic Equation.
x= -b+/- sqrt b^2-4ac/ 2a

Each equation should look like this and then solve.

x=4+sqrt -4^2-4(2)(-6)/ 2(2) x=4-sqrt -4^2-4(2)(-6)/ 2(2)

x=4 sqrt 64/4

x=3 and x=-1

I just used the quadratic formula to solve.

2x^2-4x-6=0
(x-3)(2x+2)=0
x=3 or 2x=-2
x=-1
3x^2+7x+2=0
(x+2)(3x+1)=0
x=-2 or 3x=-1
x=-1/3

2x^2-4x-6 = 0
2 (x^2 - 2x - 3) = 0
2 [x^2 - 3x + x -3] = 0
2 [x(x - 3) +1 (x - 3)]=0
2 (x - 3) (x + 1) = 0
hence x = 3, x = -1

similarly for second

3x^2 +7x+2 = 0
3x^2 + 6x + x + 2 = 0
3x (x + 2) + 1(x+2) = 0
(x+2) (3x+1) = 0
hence x = -2, and x = -1/3

x² - 2x - 3 = 0
(x - 3)(x + 1) = 0
x = 3 , x = - 1

3x² + 7x + 2 = 0
(3x + 1)(x + 2) = 0
x = - 1/3 , x = - 2