Equations Help?

Question

Hey, I'm having trouble with a few of these.

1. x^2 - 6x + 3 = 0

2. x^2 + 5x + 1 = 0

3. 2x^2 - 50 = 0

4. x = 3/x + 7

Answer 1

1. x^2 - 6x + 3 = 0
2. x^2 + 5x + 1 = 0

For these 2, use the quadratic equation, for ax^2 + bx + c = 0
x = (-b +/- (b^2 - 4ac)^1/2)/2a

1.) x = (6 +/- (36 - 12)^1/2)/2
x = 3 +/- (24)^1/2 / 2
x = 3 +/- √6

2.) x = (-5 +/- (25 - 4)^1/2)/2
x = -2.5 +/- (√21) / 2

3.) 2x^2 - 50 = 0
2 (x^2 - 25) = 0
For x^2 - a^2, factor it as (x+a)(x-a)
2(x+5)(x-5) = 0
(x+5)(x-5) = 0
x + 5 = 0, thus x = -5
x - 5 = 0, thus x = 5
Solution is x = +/- 5

4. x = 3/x + 7
Multiply everything by x:
x^2 = 3 + 7x
0 = x^2 - 7x - 3
Use the Quadratic Formula:
x = (7 +/- (49 + 12)^1/2)/2
x = 3.5 +/- (√61) / 2

Answer 2

1. x^2 - 6x + 3 = 0
First, recognize, this is a second degree polynomial. So there will be two answers. There are no integers that will multiply together and will make 3 and added together and make -6, so you have to use the quadratic equation. If you plug the numbers in, you get X=5.45 and X=0.55 (approximate)

2. x^2 + 5x + 1 = 0
Same as above.

3. 2x^2 - 50 = 0
On this one, it reduces to x^2=25, but be aware, second degree polynomial means two answers. X=5 and X=-5 would be the answer.

4. x = 3/x + 7
You must first re-arrange the formula.
X-(3/x) -7 =0
mutiply both sides by x and get:
x^2 - 3 - 7x = 0
rearrange again and you get:
x^2 - 7x -3 = 0
solve the same way as above.

Answer 3

3. 2x^2 - 50 = 0
Move the 50 to the other side of the equation, it changes signs.
2x^2 = 50
Divide through both sides by 2
x^2 = 25
Then square root both sides
x = 5

Answer 4

1. Δ=24 √Δ=2√6 x1=(6+2√3)/2=3+√6 x2=3-√6
2.Δ=21 √Δ=√21 x1=(-5+√21)/2 x2=(-5-√21)/2
3.(x-5)(x+5) x1=5 x2=-5
4.x1=(7+√61)/2 x2= (7-√61)/2

Answer 5

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