According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:

c² = a² + b²
c² = 3² + 9²
c² = 9 + 81
c² = 90
c = \( \sqrt{90} \)

To factor a quadratic expression, apply the FOIL (First, Outside, Inside, Last) method in reverse.

To solve this equation, isolate the variable for which you are solving (b) on one side of the equation and put everything else on the other side.

3b + 8x = -4b + 8x + 3
3b = -4b + 8x + 3 - 8x
3b + 4b = 8x + 3 - 8x
7b = + 3
b = \( \frac{ + 3}{7} \)
b = \( \frac{}{7} \) + \( \frac{3}{7} \)
b = x + \(\frac{3}{7}\)

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 + 2b - 9 = 5b - 5
b² + 2b - 9 + 5 = 5b
b² + 2b - 5b - 4 = 0
b² - 3b - 4 = 0

Next, factor the quadratic equation:

b² - 3b - 4 = 0
(b + 1)(b - 4) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (b + 1) or (b - 4) must equal zero:

If (b + 1) = 0, b must equal -1
If (b - 4) = 0, b must equal 4

So the solution is that b = -1 or 4

You need to find the value of b so solve the first equation in terms of z:

8b + z = 8
z = 8 - 8b

then substitute the result (8 - 8b) into the second equation:

-6b + 8(8 - 8b) = 5
-6b + (8 x 8) + (8 x -8b) = 5
-6b + 64 - 64b = 5
-6b - 64b = 5 - 64
-70b = -59
b = \( \frac{-59}{-70} \)
b = \(\frac{59}{70}\)