Note: I have numbered the exercises for clarity.
failingalgebra said:
1) Solve by factoring:
x2 – 9x = -20
My work:
x2-9x=20
+9x +9x
x2=20+9x??
To "solve", you need to start by getting everything over on one side, with "zero" on the other. Then you need to factor. Once you have the quadratic factored, you set the factors equal to zero, and solve them.
Do you know how to factor?
failingalgebra said:
2) Solve using the square root property:
5x2 = 100
Assuming "5x2" to mean "5x^2" or "5x<sup>2</sup>", a good first step would be to divide through by 5. Then, in accordance with the instructions, take the square root of each side.
You mention that you have never learned how to solve by square roots. The general process is fairly straight-forward: you have an equation of the form "(variable part)<sup>2</sup> = (number part)", and you take square roots. For instance:
. . . . .\(\displaystyle \large{x^2\,=\,9}\)
. . . . .\(\displaystyle \large{\sqrt{x^2}\,=\,\pm\sqrt{9}}\)
. . . . .\(\displaystyle \large{x\,=\,\pm3}\)
. . . . .\(\displaystyle \large{(x\,-\,3)^2\,=\,10}\)
. . . . .\(\displaystyle \large{\sqrt{(x\,-\,3)^2}\,=\,\pm\sqrt{10}}\)
. . . . .\(\displaystyle \large{x\,-\,3\,=\,\pm\sqrt{10}}\)
. . . . .\(\displaystyle \large{x\,=\,3\,\pm\,\sqrt{10}}\)
...and so forth. Apply this process to your exercise.
failingalgebra said:
3) Solve using the square root property:
(x + 8)2 = 81
2x+16=81
-16 -16
2x=65?
Is the "2" after the parentheses not a square? Is it not an exponent? (You have multiplied through by 2, rather than squaring, is why I ask.)
failingalgebra said:
4) Solve by completing the square:
x2 + 8x + 13 = 0
Are you not familiar with the process of solving by completing the square?
failingalgebra said:
5) Perform the indicated operations:
√[50] + 2√[32] – √[8]
Note that 50 = 2×5×5, 32 = 2×2×2×2×2, and 8 = 2×2×2. Use this to simplify the square roots. Then combine the "like" terms.
failingalgebra said:
6) Multiply:
(5√[2] + 3)(√[2] - 2√[3])
Just use the "FOIL" technique you learned in class.
failingalgebra said:
7) Rationalize the denominator:
2____
√[6] - √[5]
I'm sorry, but I cannot follow this. Please reply with clarification, using the formatting explained in the links in the "Forum Help" pull-down menu at the very top of the page. (Karl's Notes will probably be the easiest formatting to use.)
Thank you.
Eliz.
