okay 3 questions?

Question

1. quadratic formula to solve:
x^2-5x+6=0

#2. y^2-8y+15=0

#3. write the equation in quadratic and solve:
x(x-14)+45=0

Answer 1

OK

First one - you do not need quadratic formula, it is factorable

(x -3)(x-2) = 0 so x = 3, 2, but since you want to see quadractic:

5 +-sqrt(25 - 4(1)(6)) / 2
5 +- sqrt 1 / 2
5 + 1/2 is one 5 -1/2 is the other
6/2 = 3 is one 4/2 = 2 is the other
======================
Again, this is factorable
(x -5)(x-3)

But - since you asked:
8 +-sqrt (64 - 4(1)(15)) / 2
8 +- sqrt 4 /2
8+2/2 is one and 8-2/2 is the other
5 is one and 3 is the other
=============
x^2 -14x + 45
Again, factorable
(x-9)(x-5) - again - since you asked:

14 +-sqrt(196 - 4(1)(45))/ 2
14 +-sqrt(16)/2
14 +4 /2 is one 14-4 /2 is the other
18/2 = 9 is one, 10/2 = 5 is the other

If they are factorable, is better to factor. But if in doubt, quadratic formula always works.

Hope that helps.

Answer 2

The quadratic formula is x= (-b +/- sqrt(b^2-4ac)) / 2a

So for number 1:

x = -(-5) +/- sqrt((-5)^2 - 4(1)(6)) / 2(1)
x = 5 +/- sqrt (1) / 2
x = (5 +/- 1) / 2

From there, because you have the plus or minus, you have to split it into two equations.

x = (5 + 1) / 2 x = (5-1)/2
x = 6/2 x = 4/2
x = 3 x = 2

Your answer then is x = 3 and x = 2.


You should probably try the next two on your own to make sure you can do them. be sure for number three to first write the equation in the quadratic. This simply means to write it in ax^2+bx+c form. In your case, just multiply that x through the binomial.

I'll give you the answers I got for the next two so you can check though.

#2 x=5, x=3

#3 x= 9, x=5

Answer 3

1 x^2-5x+6=0

x = (-(-5) +/- sqrt((-5)^2 - 4(1)(6)))/(2*1)
= (5 +/- sqrt(25-24))/2
= (5 +/- sqrt(1))/2
= (5 +/- 1) / 2
= 3 or 2

2 y^2-8y+15=0
y = (-(-8) +/- sqrt((-8)^2 - 4(2)(15)))/(2*1)
= (8 +/- sqrt(64 - 60))/2
= (8 +/- sqrt(4))/2
= (8 +/- 2)/2
= 5 or 3

3 x(x-14)+45=0
x^2 - 14x + 45 = 0

x = (-(-14) +/- sqrt((-14)^2 - 4(1)(45))) / (2*1)
= (14 +/- sqrt(196 - 180))/2
= (14 +/- sqrt(16))/2
= (14 +/- 4)/2
= 5 or 9

Answer 4

1) x^2 - 5x + 6 = 0

x^2 - 2x - 3x + 6 = 0
(x - 2)(x - 3) = 0
x = 2, 3

2) y^2 - 8y + 15 = 0

y^2 - 3y - 5y + 15
(y - 3)(y - 5) = 0
y = 3, 5

3) x(x -14) + 45 = 0

x^2 -14x + 45 = 0
x^2 - 5x - 9x + 45 = 0
(x - 5)(x - 9) = 0
x = 5, 9

Answer 5

Hi,
#1
x² -5x+6=0
(x-3)(x-2)=0.... (Two factors of 6 that add up to -5)
x-3=0
x=3
x-2=0
x=2
{2,3}

#2
y²-8y +15=0
(y-3)(y-5)=0 (Two factors of 15 that add up to -8)
y-3=0
y=0
y-5=0
y=5
{3,5}

#3
x(x-14)+45 = 0
x²-14x +45 = 0....(Distributive property.)
(x-5)(x-9)=0
x-5=0
x=5
x-9=0
x=9
{5,9}

Hope this helps.
FE