Question

Does |x^2-3x+3|=3 have a solution?

Answer 1

1. Eliminate the absoulute value :

x ^ 2 - 3 x + 3 = 3

x ^ 2 - 3 x + 3 = - 3

______________________


x ^ 2 - 3 x + 3 = 3 Subtract 3 to both sides

x ^ 2 - 3 x + 3 - 3 = 3 - 3

x ^ 2 - 3 x = 0

x ( x - 3 ) = 0

Solutions :

x = 0 and x = 3



x ^ 2 - 3 x + 3 = - 3 Add 3 to both sides

x ^ 2 - 3 x + 3 + 3 = - 3 + 3

x ^ 2 - 3 x + 6 = 0

Solutions :

3 / 2 + i * sqrt ( 15 ) / 2

and

3 / 2 - i * sqrt ( 15 ) / 2


So real solutions are :

x = 0 and x = 3


P.S.

If you don't know how to solve equation

x ^ 2 - 3 x = 0

and equation

x ^ 2 - 3 x + 6 = 0


in google type:

quadratic equation online

When you see list of results click on:

Free Online Quadratioc Equation Solver:Solve by Quadratic Formula

When page be open in rectangle type your equation

and click option: solve it

You will see solution step by step.