CPhill

16-5x=4x+2        add 5x to both sides and subtract 2 from both sides

14 = 9x       divide both sides by 9

14 / 9  = x

F(x)=x^2-2x+p

F '(x)  = 2x  - 2

Set to 0, and this function has a minimum when x = 1

So

F(1)  = -2

(1)^2 - 2(1) + p = -2

1 - 2 + p = -2

-1 + p = -2    add 1 to both sides

p = -1

(a + b) (a + b)   =

Using "FOIL," we have

a^2 + ab + ab + b^2  =

a^2 + 2ab + b^2

Here you go.......good luck.....this article made my head hurt........

1 kl  x [1000m / 1 kl ] x [  39.37 in / 1 m ]  x [ 1 ft / 12 in ]  x [ 1mi / 5280 ft ] =  about .621 miles

log₆(2x-5)+1=log₆(7x+10)    note that "1 " can be written as log₆(6)  .....so we have

log₆(2x-5)+log₆(6) =log₆(7x+10)  and we can write

log₆(2x-5)(6) =log₆(7x+10)     and now, we can just solve for this

(2x - 5)(6) = (7x + 10)  simplify

12x - 30  = 7x + 10      add 30 to both sides, subtract 7x from both sides

5x = 40     divide by 5 on each side

x = 8 

1200=200+a * 4   subtract 200 from each side

1000 = 4a  divide by 4 on each side

250 = a

4.9t^2+16.2t-59.8=0

$${\mathtt{4.9}}{\mathtt{\,\times\,}}{{\mathtt{t}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{16.2}}{\mathtt{\,\times\,}}{\mathtt{t}}{\mathtt{\,-\,}}{\mathtt{59.8}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{t}} = {\mathtt{\,-\,}}{\frac{\left({\sqrt{{\mathtt{35\,863}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{81}}\right)}{{\mathtt{49}}}}\\
{\mathtt{t}} = {\frac{\left({\sqrt{{\mathtt{35\,863}}}}{\mathtt{\,-\,}}{\mathtt{81}}\right)}{{\mathtt{49}}}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{t}} = -{\mathtt{5.517\: \!863\: \!036\: \!299\: \!136\: \!9}}\\
{\mathtt{t}} = {\mathtt{2.211\: \!740\: \!587\: \!319\: \!545\: \!1}}\\
\end{array} \right\}$$

34.8 = 10.9 *t + 4.9t^2   let's mulftiply throgh by 10 to clear the decimals

348 = 109t + 49t^2   rearrange

49t^2 + 109t - 348 = 0

Using the onsite solver, we have

$${\mathtt{49}}{\mathtt{\,\times\,}}{{\mathtt{t}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{109}}{\mathtt{\,\times\,}}{\mathtt{t}}{\mathtt{\,-\,}}{\mathtt{348}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{t}} = {\frac{{\mathtt{87}}}{{\mathtt{49}}}}\\
{\mathtt{t}} = -{\mathtt{4}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{t}} = {\mathtt{1.775\: \!510\: \!204\: \!081\: \!632\: \!7}}\\
{\mathtt{t}} = -{\mathtt{4}}\\
\end{array} \right\}$$

ab + 6b = 32    →  b(a + 6)  = 32  →   b = 32/(a + 6)   (2)

Substitue (2) into (1) and we  have

a^2 + [32/(a + 6)]^2  = 20      simplify

a^2(a + 6)^2 + 1024 = 20(a+6)^2

a^2(a^2 + 12a + 36) + 1024 = 20a^2 + 240a + 720

a^4 + 12a^3 + 36a^2 + 1024 = 20a^2 + 240a + 720

a^4 + 12a^3 + 16a^2 - 240a + 304  = 0

Using the on site solver we have one real soution for a

$${{\mathtt{a}}}^{{\mathtt{4}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{12}}{\mathtt{\,\times\,}}{{\mathtt{a}}}^{{\mathtt{3}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{16}}{\mathtt{\,\times\,}}{{\mathtt{a}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{240}}{\mathtt{\,\times\,}}{\mathtt{a}}{\mathtt{\,\small\textbf+\,}}{\mathtt{304}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{a}} = {\mathtt{\,-\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{3}}}}{\mathtt{\,\times\,}}{i}{\mathtt{\,-\,}}{\mathtt{8}}\\
{\mathtt{a}} = {\mathtt{2}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{3}}}}{\mathtt{\,\times\,}}{i}{\mathtt{\,-\,}}{\mathtt{8}}\\
{\mathtt{a}} = {\mathtt{2}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{a}} = {\mathtt{\,-\,}}{\mathtt{8}}{\mathtt{\,-\,}}{\mathtt{3.464\: \!101\: \!615\: \!137\: \!754\: \!6}}{i}\\
{\mathtt{a}} = {\mathtt{\,-\,}}{\mathtt{8}}{\mathtt{\,\small\textbf+\,}}{\mathtt{3.464\: \!101\: \!615\: \!137\: \!754\: \!6}}{i}\\
{\mathtt{a}} = {\mathtt{2}}\\
\end{array} \right\}$$

And b =

32 /(a + 6)   = 32 /(2 + 6)  =  32 /8   = 4