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yes, it is   - 7/4   or   - 1.75

d is $\sqrt{\frac{293}{3}}$

Firstly, we factor this equation as $a(x + 6) = -x^2.$  Because $-x^2 \ne (-x)^2,$ we have $a(x+6)=-1(x^2),$ so $a(-x-6)=x^2.$ 

There are 18 integer solutions. Only 1 is positive for a, and two are non negative.

x=−(7/4)?

Square both sides of the equation to get

9 (x+2) = x+4

9x+18 = x+4

8x = 4-18                   I think you can finish !

3 (x^2+2/3x)   - 4         'complete the square'

3 (x+1/3)^2   - 4 1/3   

5x^2-80x+18 = 0     Quadratic Formula shows roots   x =   8 +- sqrt (1510) / 5

   take it from here......

1 - 2013^2013 mod 13 = 8 - the remainder.

2 - 17^77 mod 35 = 12 - the remainder

3 - There are NO "n" less than 100 that are multiples of 6.

4 - The smallest positive multiple of 21 that has no digits larger than 1 ==101010

The sum of ALL digits from 1 to 170 inclusive =1,503

There are 118 rectangles in the grid.

here are 4 lines on the 3 x 3  page encompassing 12 borders ....  18 / 12 =  1.5 inch side length of stamp

the 6 x 6 will have 10 lines  each covering 6 edges     6 edges x 1.5 inches x 10 = 90 inches

1 - n = 10! =3,628,800  and (10+1)! = 11! =39,916,800

2 - N=1991*1993*1995*1997*1999 = N = 31601836203377055. Sum = 0 + 5 + 5 = 10

3 - sumfor(n, 1, 50, 2*n) = 2550 mod 7 = 2 - the remainder

259  268  277  286  295  > Total = 5 such numbers

OK thanks 

First one   5 .678     nearest whole number  6  (round UP from .5 or above)     nearest 10th  5.7    nearest 100th 5.68

   you try the rest......let us know if you need more help

Well 79.95   is really just ~ 80

  and 45.25 is about  ~ 45       so she spent about     80+45 = $125

80 - 45 = ~$35 more on skates

I get the following:

x=(2^2017+3^2017)*(4^2017+5^2017);print x;y=(2^2017+4^2017)*(3^2017+5^2017);printy;z=(2^2017+5^2017)*(3^2017+4^2017);printz

y = 1.504877865 E+2624
z = 1.504877865 E+2624

x = 1.499924902 E+2372

Note: y and z are equivalent. You may arrange them the way they want.

The last digit is a 2, found as follows:

From 1 to 9          = 1 time
From 10 to 99      =19 times
From 100 to 600  =20 x 5 =100 times
1 + 19 + 100 =120 times between 1 and 600
Note: This counts repeated 9's such as 99, 199....etc.