hectictar

The fastest way is with factoring.

x² + 5x + 6 = 0

(x+2)(x+3) = 0

Set each factor equal to zero.

x + 2 = 0       and      x + 3 = 0

x = -2            and      x = -3

You can also use the quadratic formula.

\(ax^{2}+bx+c=0 \\ x = {-b \pm \sqrt{b^2-4ac} \over 2a} \\ a=1, b=5, c=6 \\ x = {-5 \pm \sqrt{5^2-4(1)(6)} \over 2(1)} \\ x = {-5 \pm \sqrt{1} \over 2} \\ x = \frac{-5+1}{2} \text{ and } x = \frac{-5-1}{2} \\ x=-2 \text{ and } x=-3\)

A third method is called completing the square, here's an explanation of that method:

https://www.youtube.com/watch?v=bNQY0z76M5A

\(\sqrt{5^{2}}+2^{2} = 5+4 =9\)

To solve for x, subtract 30 from both sides then divide both sides by 5.

5x + 30 = 0

5x = -30

x = -6

700,000 + 5,000x = y

and 

600,000 + 10,000x = y

So

600,000 + 10,000x = 700,000 + 5,000x

Solve for x:

10,000x = 100,000 + 5,000x

5,000x = 100,000

x = 20

Plug in x to find y:

700,000 + 5,000(20) = y

700,000 + 100,000 = y

800,000 = y

\(7\frac{3}{8} = \frac{59}{8} = 7.375\)

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Don't forget to put parenthesees around it if necessary.

\(4\frac{1}{2} + 9\frac{1}{8} \\ = 4\frac{4}{8} + 9\frac{1}{8} \\ = 13\frac{5}{8}\)

I think we need one more piece of information about the triangle.

Yes they are equal. When you have a negative exponent on a term in the numerator you can move that term to the denominator and get rid of the negative sign on the exponent. 2^-3 = 1/2³

tan x = 18/22

arctan(tan x) = arctan(18/22)

x ≈ 39.289º