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:

x² + x - 44 = 2x - 2
x² + x - 44 + 2 = 2x
x² + x - 2x - 42 = 0
x² - x - 42 = 0

Next, factor the quadratic equation:

x² - x - 42 = 0
(x + 6)(x - 7) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (x + 6) or (x - 7) must equal zero:

If (x + 6) = 0, x must equal -6
If (x - 7) = 0, x must equal 7

So the solution is that x = -6 or 7

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, \(c = \sqrt{a + b}\)

The area of a triangle is equal to ½ base x height:

a = ½bh
a = ½ x 2 x 4 = \( \frac{8}{2} \) = 4

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.

3x + 8 < \( \frac{x}{-2} \)
-2 x (3x + 8) < x
(-2 x 3x) + (-2 x 8) < x
-6x - 16 < x
-6x - 16 - x < 0
-6x - x < 16
-7x < 16
x < \( \frac{16}{-7} \)
x < -2\(\frac{2}{7}\)

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

c² = a² + b²
c² = 4² + 9²
c² = 16 + 81
c² = 97
c = \( \sqrt{97} \)