3x2+2x-8=0 Delta = 22-4*3*-8= 100 So x = (-2 + sqrt(100))/(2*3) or x = (-2 - sqrt(100))/(2*3) x = 4/3 or x=-2
3x2 - 19x - 14 = 0 3x2 - 21x + 2x - 14 = 0 3x(x - 7) + 2(x - 7) = 0 (x - 7)(3x + 2) = 0 x - 7 = 0 or 3x + 2 = 0 x = 7 or x = -2/3
Assuming that 4x2+2x = 0: 2x (2x+1) = 0 2x = 0 or 2x+1 = 0 x = 0 or -1/2
3x2-4x-15 = 0 (3x+5)(x-3) = 0 x = -5/3 or x = 3
2x = -7 - 8y
3x2 + 2x - 8 = 0 is a quadratic equation.
3x2 + 2x = 16 ∴ 3x2 + 2x - 16 = 0 ∴ 3x2 - 6x + 8x - 16 = 0 ∴ 3x(x - 2) + 8(x - 2) = 0 ∴ (3x + 8)(x - 2) = 0 ∴ x ∈ {-8/3, 2}
3x3 -3x2 - 48x - 60 = 0 simply factor out a 3... 3(x3 - x2 - 16x - 20) = 0
5x3 - 3x2 + 2x = x*(5x2 - 3x + 2) The quadratic has no real factors.
x2+8x = -3x2+5 4x2+8x-5 = 0 (2x+5)(2x-1) = 0 x = -5/2 or x = 1/2
(2x-4)(x-1) = 0
x squared -2x-3 equals 0 is the same as (x + 1)(x - 3) = 0
2x^2 + 8x + 3 = 0
3x2 - 2x - 5 = (3x - 5)(x + 1) = 0 gives a solution of x = 5/3 or -1. Was that what you wanted?
(2x + 3)(2x + 3)
6x-6x=0 so all you have left is -16 and there is nothing to factor. I am guessing you meant 6x2 -6x-16 which is 2(3x2 -2x-8) The factor pairs for 8 are 1,8 and 2,4. So let's try 1, 8. We know one of them has to be negative. We see it does not work and when we try 2 and 4 they do not work also. So we cannot factor (3x2 -2x-8) over the integers and we call it prime. The final answer is 2(3x2 -2x-8)
3x(2x + 1)