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:

z² - 5z - 13 = -z - 1
z² - 5z - 13 + 1 = -z
z² - 5z + z - 12 = 0
z² - 4z - 12 = 0

Next, factor the quadratic equation:

z² - 4z - 12 = 0
(z + 2)(z - 6) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (z + 2) or (z - 6) must equal zero:

If (z + 2) = 0, z must equal -2
If (z - 6) = 0, z must equal 6

So the solution is that z = -2 or 6

The surface area of a cylinder is 2πr² + 2πrh:

sa = 2πr² + 2πrh
sa = 2π(6²) + 2π(6 x 8)
sa = 2π(36) + 2π(48)
sa = (2 x 36)π + (2 x 48)π
sa = 72π + 96π
sa = 168π

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.

2b - z = 8b - 8z - 4
2b = 8b - 8z - 4 + z
2b - 8b = -8z - 4 + z
-6b = -7z - 4
b = \( \frac{-7z - 4}{-6} \)
b = \( \frac{-7z}{-6} \) + \( \frac{-4}{-6} \)
b = 1\(\frac{1}{6}\)z + \(\frac{2}{3}\)

The circumference of a circle is the distance around its perimeter and equals π (approx. 3.14159) x diameter: c = π d. The area of a circle is π x (radius)² : a = π r².

A line segment is a portion of a line with a measurable length. The midpoint of a line segment is the point exactly halfway between the endpoints. The midpoint bisects (cuts in half) the line segment.