The first step to solve a quadratic expression that's not set to zero is to solve the equation so that it is set to zero:

b² - 8b + 38 = 5b + 2
b² - 8b + 38 - 2 = 5b
b² - 8b - 5b + 36 = 0
b² - 13b + 36 = 0

Next, factor the quadratic equation:

b² - 13b + 36 = 0
(b - 4)(b - 9) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (b - 4) or (b - 9) must equal zero:

If (b - 4) = 0, b must equal 4
If (b - 9) = 0, b must equal 9

So the solution is that b = 4 or 9

To multiply monomials, multiply the coefficients (the numbers that come before the variables) of each term, add the exponents of like variables, and multiply the different variables together.

(8a)(7ab) + (8a²)(8b)
(8 x 7)(a x a x b) + (8 x 8)(a² x b)
(56)(a¹⁺¹ x b) + (64)(a²b)
56a²b + 64a²b
120a²b

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° - 63° - 44° = 73°

So, d° = 44° + 73° = 117°

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° - 63° = 117°

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\( \sqrt{2} \)

The entire length of this line is represented by AD which is AB + BD:

AD = AB + BD