To factor a quadratic expression, apply the FOIL method (First, Outside, Inside, Last) in reverse. First, find the two Last terms that will multiply to produce 8 as well and sum (Inside, Outside) to equal -9. For this problem, those two numbers are -8 and -1. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² - 9y + 8
y² + (-8 - 1)y + (-8 x -1)
(y - 8)(y - 1)

A right angle measures 90 degrees and is the intersection of two perpendicular lines. In diagrams, a right angle is indicated by a small box completing a square with the perpendicular lines.

A circle is a figure in which each point around its perimeter is an equal distance from the center. The radius of a circle is the distance between the center and any point along its perimeter. A chord is a line segment that connects any two points along its perimeter. The diameter of a circle is the length of a chord that passes through the center of the circle and equals twice the circle's radius (2r).

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:

a² + 10a + 13 = 2a + 1
a² + 10a + 13 - 1 = 2a
a² + 10a - 2a + 12 = 0
a² + 8a + 12 = 0

Next, factor the quadratic equation:

a² + 8a + 12 = 0
(a + 2)(a + 6) = 0

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

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

So the solution is that a = -2 or -6

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

c² = a² + b²
c² = 8² + 5²
c² = 64 + 25
c² = 89
c = \( \sqrt{89} \)