Need help with these quadratic problems.?

Question

I am not sure how to type out squared on the computer but here we go.... please show your work to and any explainations.

1) 9x(squared) + 5x + 3 = 0

2) 4x(squared) - 4x + 2 = 0

thanks

Answer 1

Well usually you can note exponents by using the carrot key (^)
like 5(squared) is understood from 5^2

And for both of these problems you can use the quadratic formula.
in any general formula, ax^2 + bx + c = 0
x = (-b +/- sqrt(b^2 - 4ac)) / 2a

so both of these just plug into the formula.

1. 9x^2 +5x + 3 = 0
x = (-5 +/- sqrt(-83)) / 18
so since there's a negative value in the square root, the two answers for this are imaginary numbers
x1 = (-5 + i*rt(83)) / 18
x2 = (-5 - i*rt(83)) / 18

2. for this one you can first divide by 2 on both sides.
2x^2 - 2x +1 = 0
again use the quadratic formula:
x = (2 +/- rt(4 - 8)) / 4
x = (2 +/- rt(-4)) / 4
x = (2 +/- 2i) / 4
x = (1 +/- i) / 2
so the two answers are:
x1 = 1/2 + i/2
x2 = 1/2 - i/2

Answer 2

Question 1
9x² + 5x + 3 = 0
x = [ - 5 ± √(25 - 108) ] /18
x = [- 5 ± √(- 83) ] / 18
x = [- 5 ± i √(83) ] / 18

Question 2
2x² - 2x + 1 = 0
x = [ 2 ± √(4 - 8) ] / 4
x = [ 2 ± √(- 4)] / 4
x = [ 2 ± 2i ] / 4
x = (1/2) (1 ± i )