The first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:

c² + 6c - 16 = 0
(c - 2)(c + 8) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (c - 2) or (c + 8) must equal zero:

If (c - 2) = 0, c must equal 2
If (c + 8) = 0, c must equal -8

So the solution is that c = 2 or -8

The surface area of a cube is (2 x length x width) + (2 x width x height) + (2 x length x height):

sa = 2lw + 2wh + 2lh
sa = (2 x 6 x 5) + (2 x 5 x 9) + (2 x 6 x 9)
sa = (60) + (90) + (108)
sa = 258

The area of a rectangle is equal to its length x width:

a = l x w
a = a x b
a = 9 x 1
a = 9

To find the diagonal we need to know the length of one of the square's sides. We know the area and the area of a square is the length of one side squared:

a = s²

so the length of one side of the square is:

s = \( \sqrt{a} \) = \( \sqrt{16} \) = 4

The Pythagorean theorem defines the square of the hypotenuse (diagonal) of a triangle with a right angle as the sum of the squares of the other two sides:

c² = a² + b²
c² = 4² + 4²
c² = 32
c = \( \sqrt{32} \) = \( \sqrt{16 x 2} \) = \( \sqrt{16} \) \( \sqrt{2} \)
c = 4\( \sqrt{2} \)

An exterior angle of a triangle is equal to the sum of the two interior angles that are opposite:

d° = b° + c°

To find angle c, remember that the sum of the interior angles of a triangle is 180°:

180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 49° - 59° = 72°

So, d° = 59° + 72° = 131°

A shortcut to get this answer is to remember that angles around a line add up to 180°:

a° + d° = 180°
d° = 180° - a°
d° = 180° - 49° = 131°