Algebra: Chapter 13-3, p 586
Solving quadratics by completing the squares
We can use the technique of completing the square to solve quadratic equations. Recall that the addition property allows us to add a number to both sides of the equation. To complete a square, take 1/2 of the x-coefficient, square it and add it to both sides of the quadratic equation.
For example:
`x^2 – 4x – 7 = 0` becomes `x^2 – 4x = 7` by adding 7 to both sides.
`x^2 – 4x + 4 = 7 + 4` by adding 4 to both sides to complete the square.
`(x – 2)^2 = 11` or by square rooting each side to `x – 2 = ±sqrt(11)` so that
`x = 2 ± sqrt(11)` or `2 + sqrt(11)` and `2 – sqrt(11)` as the final solutions.
Purplemath explains it too, just click here for step-by-step instructions.
Math-8: Chapter 12-5, p 632
Surface Area: Prisms and Cylinders
Prisms, be they rectilinear (rectangular) or triangular (triangles) have sides, called “faces” and points, called “vertices” and “edges”. You can figure out the “SURFACE AREA” of a prism by taking the sides apart one at a time and treating them as either rectangles or triangles. Remembering the formulas for area of a rectangle as area `a =l⋅w` and the area of a triangle as area `a=(1/2)(b⋅h)` can give you all the tools you need to find the surface area.
For cylinders, its a little different. The end caps are easy, they are just the area of the disk or circle. The area of a circle is Area `a=πr^2` or `a=πd` because `2r=d`. For the side of the cylinder, just “unroll” the tube. The circumference of the end caps, is the length of the rectangle formed during the unrolling of the tube. Remember, circumference, `c=2πr`.
If you can visualize, or take apart the prism or cylinder, those pieces layed out on the floor are called a NET. The surface area of the object becomes the surface area of the NET.
Here is a link to purplemath.com with the formulas laid out nice and neat.