Category: Grade 11

x squared + 8x + 2 =22 (example)

we divide 8 by 2 and then square it, so that becomes 4 squared and then 16. After that we use a zero pair so 16 – 16, so that means x squared + 8x + 16 – 16 +2 = 22. x squared + 8x +16 equals to (x+4) squared. (x+4) squared – 14 = 22. (x+4) squared = 36. Take the roots of both sides, that leaves (x+4) = root 36. x+4 equals +-6. X1 = -10, X2 = 2.

for dividing, you basically make the denominator a rational number. For binomials, you conjugate. At the end, the denominator has to be rationalized. Down below is an example. We multiplied root 5 by the denominator to make it 5 and since we multiplied root 5 with the denominator, we had to multiply it with the numerator too.

This week, I learned how to identify values of variables like x E R, x < 0, x > 0, etc.

for example , the x has to be positive because you cant put negative numbers in square root. so that means x >/ 0, x has to be equal or bigger than 0.

This week I learned that if a numbers index is even like 2, there cant be a negative sign in the root because negatives dont have an even root so it makes it impossible, but if the index is odd like 3, you can still put the negative sign in the root.

examples: is impossible because the index is 2 which is even (it is invisible).

is possible because the index is 3 which is odd.

This week, I learned how to solve numbers with fraction exponents. For example, . you write down the base, which is 3, then make a square root so the 2 in the exponent becomes the index and the 1 stays as the exponent. At the end, it would be (the index is 2 but it is invisible and = 3 so no need to write down the 1.)