Question

Help needed on highlighted questions! 20 points

Answer 1

For this case we must solve the following questions:

Question 1:

We must solve the following quadratic equation:

`x ^ 2 + 1 = 0`

We subtract 1 from both sides of the equation:

`x ^ 2 + 1-1 = -1\\x ^ 2 = -1`

We apply square root to eliminate the exponent:

`x = \pm \sqrt {-1}`

The solution is not real.

`x_ {1} = + i\\x_ {2} = - i`

Answer:

`x_ {1} = + i\\x_ {2} = - i`

Option D

Question 2:

We must solve the following quadratic equation:

`x ^ 2-10x + 24 = 0`

We factor the equation, that is, we must look for two numbers that when multiplied give as result 24 and when summed with -10. These numbers are -6 and -4:

`-6-4 = -10\\-6 * -4 = 24\\(x-6) (x-4) = 0`

The roots are:

`x_ {1} = 6\\x_ {2} = 4`

ANswer:

`x_ {1} = 6\\x_ {2} = 4`

Option D

Question 3:

We must complete squares of the following expression:

`x ^ 2-18x = 7`

We add
`(\frac {b} {2}) ^ 2 = (\frac {-18} {2}) ^ 2 = (- 9) ^ 2`

Then:

`x ^ 2-18x + (- 9) ^ 2 = 7 + (- 9) ^ 2\\x ^ 2-18x + (- 9) ^ 2 = 7 + 81\\x ^ 2-18x + (- 9) ^ 2 = 88\\(x-9) ^ 2 = 88`

Then, to complete the square, add it to both sides
`(-9) ^ 2 = 81`

Answer:

Option C