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 30 as well and sum (Inside, Outside) to equal 11. For this problem, those two numbers are 5 and 6. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² + 11y + 30
y² + (5 + 6)y + (5 x 6)
(y + 5)(y + 6)

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

c² = a² + b²
c² = 7² + 3²
c² = 49 + 9
c² = 58
c = \( \sqrt{58} \)

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

c² - 4c - 5 = 0
(c + 1)(c - 5) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (c + 1) or (c - 5) must equal zero:

If (c + 1) = 0, c must equal -1
If (c - 5) = 0, c must equal 5

So the solution is that c = -1 or 5

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.

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).