Question

Solve the equation for x, where x is a real number:
-10x^2 + 3x - 2 = 0

Answer 1

More analytically, we can apply the quadratic formula to find the solutions. This quadratic formula solves equations of the form ax^2 + bx + c = 0
x = [ -b ± √(b^2 - 4ac) ] / (2a)
x = [ -3 ± √((3)^2 - 4(-10)(-2)) ] / ( 2(-10) )
x = [-3 ± √(9 - (80) ) ] / ( -20 )
x = [-3 ± √(-71) ] / ( -20)
Since √-71 is a nonreal number, there are no real solutions to this equation.

Answer 2

The equation has no real solutions. (There are no x-intercepts.)

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The complex solutions are x = 0.15 ±i√0.1755.