The Pythagorean theorem defines the relationship between the side lengths of a right triangle. The length of the hypotenuse squared (c²) is equal to the sum of the two perpendicular sides squared (a² + b²): c² = a² + b² or, solved for c, \(c = \sqrt{a + b}\)

A quadrilateral is a shape with four sides. The perimeter of a quadrilateral is the sum of the lengths of its four sides.

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:

c² - 2c + 6 = c + 4
c² - 2c + 6 - 4 = c
c² - 2c - c + 2 = 0
c² - 3c + 2 = 0

Next, factor the quadratic equation:

c² - 3c + 2 = 0
(c - 1)(c - 2) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (c - 1) or (c - 2) must equal zero:

If (c - 1) = 0, c must equal 1
If (c - 2) = 0, c must equal 2

So the solution is that c = 1 or 2

To multiply binomials, use the FOIL method. FOIL stands for First, Outside, Inside, Last and refers to the position of each term in the parentheses.

To solve this equation, repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the < sign and the answer on the other.

8a + 7 < \( \frac{a}{2} \)
2 x (8a + 7) < a
(2 x 8a) + (2 x 7) < a
16a + 14 < a
16a + 14 - a < 0
16a - a < -14
15a < -14
a < \( \frac{-14}{15} \)
a < -\(\frac{14}{15}\)