College Alebra Question PLEASE SHOW ALL WORK do NOT skip or

College Alebra Question. PLEASE SHOW ALL WORK (do NOT skip or combine any steps). I know the answer but I don\'t know how they arrived at that answer.

Again, I need to see ALL of the steps for how to arrive at this answer.

20. Find all solutions to x x 2 0 ANSWER 1,1 i, 1 i

Solution

x³ -x² + 2 = 0 or, x³ + x² - 2x² +2 = 0 or, x²(x +1) -2(x² -1) = 0 or, x²(x +1) -2(x+1)(x-1) = 0 or, (x+1)[x² -2(x -1)] = 0 or, (x+1)( x² - 2x + 2) = 0 . Therefore, either (x +1) = 0, in which case, x = -1; or, x² -2x + 2 = 0. Now, if x² -2x + 2 = 0, then using the quadratic formula, x = [ -(-2) ± { (-2)² -4*1*2} ]/ 2*1 or, x = [ 2 ± ( 4 - 8)]/2 or, x = [ 2 ± (-4)]/2 or, x = ( 2 ± 2i)/2 = 1± i. ( as -1 = i). Thus, the answers are x = -1, 1+ i and 1 - i.

Note: The solution to ax² +bx + c = 0 are x = [ -b ± (b² -4ac) ]/2a . This is the quadratic formula.