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 - 5a - 24 = a + 3
a² - 5a - 24 - 3 = a
a² - 5a - a - 27 = 0
a² - 6a - 27 = 0

Next, factor the quadratic equation:

a² - 6a - 27 = 0
(a + 3)(a - 9) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (a + 3) or (a - 9) must equal zero:

If (a + 3) = 0, a must equal -3
If (a - 9) = 0, a must equal 9

So the solution is that a = -3 or 9

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 = \( \sqrt{a} \) = \( \sqrt{25} \) = 5

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 = 5² + 5²
c² = 50
c = \( \sqrt{50} \) = \( \sqrt{25 x 2} \) = \( \sqrt{25} \) \( \sqrt{2} \)
c = 5\( \sqrt{2} \)

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.

5a - 4 > -5 + 2a
5a > -5 + 2a + 4
5a - 2a > -5 + 4
3a > -1
a > \( \frac{-1}{3} \)
a > -\(\frac{1}{3}\)

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.

The slope of this line is the change in y divided by the change in x. The endpoints of this line segment are at (-2, -6) and (2, 6) so the slope becomes: