Quadratic formulas again..?

Question

The quadratic formula: Solve the quadratic equation by using the quadratic formula. If the
roots are irrational, give the rational approximations to the nearest tenth.

1. 7x^2+3x=0

{___,___}

2. (x-2)(x-3) = 2

{___,___}

Thank you!

Answer 1

Answer 1:
7x^2 + 3x = 0

x = [-3 +/- (sqrt 9)]/14
x = [-3 +/- 3]/14
x = 0/14 (or) x = -6/14
x = 0, -3/7

{0, -3/7}

Answer 2:
(x - 2)(x - 3) = 2
x^2 - 5x + 6 = 2
x^2 - 5x + 4 = 0

x = [5 +/- sqrt (25 - 16)]/2
x = [5 +/- sqrt (9)]/2
x = (5 +/- 3)/2
x = 8/2 (or) x = 2/2
x = 4, 1

{4, 1}

Answer 2

the quadratic formula is: -b +/- square root of b^2 - 4ac/2a

it's hard to follow here but . . . give it your best shot.

1) -3 +/- square root 3^2 - 4(7)(0)/2(7)
-3 +/- square root 9 - 0/14
-3 +/- 3/14
{0, -9/14}

2) you don't really need the quadratic formula for this one, but if it's required, you must distribute first. just so you know the answer is: {2, 3}. But I will show you how to do it with the quadratic formula.

x^2 - 5x + 6
5+/- square root -5^2 - 4(1)(6)/2(1)
5 +/- square root 25 - 24/2
5 +/- square root 1/2
(5+1)/ = 3
(5-1)/2 = 2
{3,2}

Answer 3

purely sing this to the music of "Pop, is going the Weasel", and you optimistically won't forget the formula: X equals the different of B plus-minus the sq. root of B squared minus 4 A C throughout 2 A.

Answer 4

1. 0 and 1.56

2. 4 and 5