An isosceles triangle has two sides of equal length. An equilateral triangle has three sides of equal length. In a right triangle, two sides meet at a right angle.

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 + 8x - 43 = 5x - 3
x² + 8x - 43 + 3 = 5x
x² + 8x - 5x - 40 = 0
x² + 3x - 40 = 0

Next, factor the quadratic equation:

x² + 3x - 40 = 0
(x - 5)(x + 8) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (x - 5) or (x + 8) must equal zero:

If (x - 5) = 0, x must equal 5
If (x + 8) = 0, x must equal -8

So the solution is that x = 5 or -8

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).

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 entire length of this line is represented by AD which is AB + BD:

AD = AB + BD