Solve the equation by the method of your choice. Simplify solutions, if possible?

Question

12x^2 + 28x - 1 = -16

Is it - 2/3, -5/6?

Answer 1

1.12x^2+28x+15=0
12x^2+18x+10x+15=0
6x(2x+3)+5(2x+3)=0
(2x+3)(6x+5)=0
x=-3/2 or -5/6

Answer 2

12x^2 + 28x - 1 = -16

First, bring that -16 over to the left hand side,

12x^2 + 28x + 15 = 0

And now, we factor. It's tricky because 12, the coefficient of x^2, has many factors. 12 = 6 x 2, 3 x 4. So it's better off to just use the quadratic formula.

x = [-b +/- sqrt(b^2 - 4ac)]/2a
x = [-28 +/- sqrt(784 - 720)]/24
x = [-28 +/- sqrt(64)]/24 {At this point, we should be going, WOO HOO! We have a perfect square! sqrt(64) = 8!}

x = [-28 +/- 8]/24

I forgot to note that "+/-" means "plus or minus".

Therefore, x = [-28 + 8]/24 and [-28 - 8]/24, OR

x = -20/24 = -5/6
x = -36/24 = -3/2
x = -5/6, -3/2

Answer 3

2(x-a million)^2 - 3= 40 seven (move all knowns on one area, unknowns to the different) 2(x-a million)^2 = 40 seven+3 2(x-a million)^2 = 50 /:2 (x-a million)^2 = 25 (I see a achievable for the version of squares the following, ie. x^2-y^2 = (x-y)(x+y), which will provide us the options with out meddling with the quadratic equation and roots) (x-a million)^2 - 25 = 0 (x-a million)^2 - 5^2 = 0 (x-a million-5)(x-a million+5) = 0 (x-6)(x+4) = 0 x-6 = 0 x = 6 plug this contained in the equation, for checking: 2(x-a million)^2 - 3= 40 seven 2(6-a million)^2 - 3 = 40 seven 2*5^2 - 3 = 40 seven 2*25 - 3 = 40 seven 50-3 = 40 seven 40 seven = 40 seven ok! x+4 = 0 x = -4 examine: 2(-4-a million)^2 - 3= 40 seven 2*(-5)^2 - 3 = 40 seven 2*25 - 3 = 40 seven 50-3 = 40 seven 40 seven = 40 seven ok! the answer's {-4, 6}

Answer 4

12x^2 +28x -1 = -16
12x^2 +28x + 15 = 0
(6x + 5)(2x + 3) = 0

x = -3/2, -5/6

One of your answers is correct, the other is inverted.

Answer 5

x=-5/6 x=-1.5