35a^2 - 12a - 4 = 0?

Answer 1

*Use the Quadratic Formula: x = [- b +/- V`b^2 - 4ac] / 2a

First: you need three values for three variables..
a = 35 > b = -12 and > c = - 4

Sec: replace the values with their corresponding variables...

x = [- b +/- V`b^2 - 4ac] / 2a

x = [- (-12) +/- V`(-12)^2 - 4(35)(-4)] / 2(35)

x = [12 +/- V`(-12^2) - 4(35)(-4)] / 70

x = [12 +/- V`144 - 4(35)(-4)] / 70

x = [12 +/- V`144 - 4(-140)] / 70

x = [12 +/- V`144 + 560] / 70

x = [12 +/- V`704] / 70

x = [12 +/- V`2*2*2*2*2*2*11] / 70

x = [12 +/- 2*2*2 V`11] / 70

x = [12 +/- 8 V`11] / 70

Third: you have two solutions, one has addition-the other has subtraction...

1. x = [12 + 8 V`11] / 70
x = 12/70 + (8 V`11)/70
x = 6/35 + (8 V`11)/70

2. x = [12 - 8 V`11] / 70
x = 12/70 - (8 V`11)/70
x = 6/35 - (8 V`11)/70

Solutions: 6/35 + (8 V`11)/70 and 6/35 - (8 V`11)/70

Answer 2

Not nice! (It doesn't factorize.) From the standard form for the solution to a quadratic equation there are two solutions. Written compactly (wth +/- ) they are:

a = [12 +/- sqrt(144 + 16x35)] / 70 = [12 +/- 26.5330...] / 70.

So the two roots are:

+ 0.5505 and - 0.2076 (to 4 significant figures).

CHECK: inserting these values into the original quadratic equation, it's satisfied with small residuals in the 4th place beyond the decimal point, as expected due to the rounding error in the numerical solutions given above. (It's always worthwhile to do such a check, to confirm that one hasn't made some algebraic slip in writing down the solutions.)

[Later edit: You could also write them as [6 +/- 4sqrt(11)] / 35.
Tom: sorry, but you divided by "-8" or "2c" in the standard notation. That should have been "2a" or "+ 70". You also dropped a "-" sign on going to the last line; your own answer should have started with
"-3/2," not just "3/2". 'singingrose21': your two "8/70" factors can be simplified to 4/35.]

[STILL LATER EDIT: Tom, you "corrected" your "-8" error INCORRECTLY! You've NOW divided by "-70" instead of "+70" --- I'm afraid that it's time to give up!]

Live long and prosper.

Answer 3

35a² - 12a - 4 = 0

x = 35
y = -12
z = -4

a = [-y ± √(y² - 4xz)]/2*-35
a = [12 ± √(144 + 560)]/70
a = [12 ± √(704)]/70
a = [12 ± √(64*11)]/70
a = [12 ± 8√11]/70
a = (6 ± 4√11)/35

Answer 4

a = 0.55, -0.21 (both rounded)