Question

Solve the equation for x, where x is a real number (5 points):
3x^2 - 2x + 2 = 5

Answer 1

Subtract 5 to both sides to the equation becomes 3x^2 - 2x - 3 = 0

To solve this equation, we can use the quadratic formula. The quadratic formula solves equations of the form ax^2 + bx + c = 0
x = [ -b ± √(b^2 - 4ac) ] / (2a)
x = [ --2 ± √((-2)^2 - 4(3)(-3)) ] / ( 2(3) )
x = [ 2 ± √(4 - (-36) ) ] / ( 6 )
x = [ 2 ± √(40) ] / ( 6)
x = [ 2 ± 2*sqrt(10) ] / ( 6 )
x = 1/3 ± sqrt(10)/3
The answers are 1/3 + sqrt(10)/3 and 1/3 - sqrt(10)/3.

Answer 2

Subtract 5, then use the quadratic formula to find ths solutions.
3x^2 -2x -3 = 0
x = (-(-2) ±√((-2)^2 -4(3)(-3)))/(2(3))
x = (2 ±√40)/6 = (1 ±√10)/3

The solutions are x = (1 ±√10)/3 ≈ {-0.720759, 1.387426}