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 - 2z - 38 = 3z - 2
z² - 2z - 38 + 2 = 3z
z² - 2z - 3z - 36 = 0
z² - 5z - 36 = 0

Next, factor the quadratic equation:

z² - 5z - 36 = 0
(z + 4)(z - 9) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (z + 4) or (z - 9) must equal zero:

If (z + 4) = 0, z must equal -4
If (z - 9) = 0, z must equal 9

So the solution is that z = -4 or 9

An acute angle measures less than 90°, a right angle measures 90°, and an obtuse angle measures more than 90°.

To solve this equation, replace the variables with the values given and then solve the now variable-free equation. (Remember order of operations, PEMDAS, Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.)

6c(c - y)
6(6)(6 - 6)
6(6)(0)
(36)(0)
0

The area of a rectangle is equal to its length x width:

a = l x w
a = a x b
a = 7 x 4
a = 28

To find the diagonal we need to know the length of one of the square's sides. We know the area and the area of a square is the length of one side squared:

a = s²

so the length of one side of the square is:

s = \( \sqrt{a} \) = \( \sqrt{4} \) = 2

The Pythagorean theorem defines the square of the hypotenuse (diagonal) of a triangle with a right angle as the sum of the squares of the other two sides:

c² = a² + b²
c² = 2² + 2²
c² = 8
c = \( \sqrt{8} \) = \( \sqrt{4 x 2} \) = \( \sqrt{4} \) \( \sqrt{2} \)
c = 2\( \sqrt{2} \)