Solve 3x^{2} + 6x + 6 = 0 using the quadratic formula.

Question

please answer the entire question

Answer 1

You DO NOT NEED those curly braces...AVOID them (the general idea being to minimize obfuscation).

 

First, observe that you can divide this quadratic equation by 3 and get a simpler x² + 2x + 2 = 0.

 

Could you factor this?  NO...so the quadratic formula should be used.  Proceed!

Answer 2

The quadratic formula is as follows:

when ax² + bx + c = 0, then

x = (-b ± √(b² - 4ac)) / 2a

 

Step one is to put in the matching coefficients into the formula:

x = (-6 ± √(6² - 4 * 3 * 6) / (2 * 3)

 

x = (-6 ± √(36 - 72) / 6

x = (-6 ± √-36) / 6

 

Normally, we cannot get the square root of a negative, but as this is algebra 2, I don't know if you have learned about i yet. If not, then your answer is undefined. If so, we can keep going:

x = (-6 ± (√36 * √-1)) / 6

x = (-6 ± 6i) / 6

x = 6(-1 ± i) /6

x = -1 ± i