SOLUTION: Explain why the equation (x-1)^2 +(x+1)^2 = 0 has no real roots. Can you please help me out? Thanks so much in advance :)

Question 807901: Explain why the equation (x-1)^2 +(x+1)^2 = 0 has no real roots.
Can you please help me out? Thanks so much in advance :)
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
(x-1)^2 +(x+1)^2 = 0

x^2 - 2x + 1 + x^2 + 2x + 1 = 0 ... FOIL/expand

2x^2 + 2 = 0 ... Combine like terms.

2x^2 = -2 ... Subtract 2 from both sides.

x^2 = -2/2 ... Divide both sides by 2.

x^2 = -1

So at this point, we can see that the equation won't have any real roots. Why? Because solving x^2 = -1 gives us x = i or x = -i, both of which are not real.

Note: which is an imaginary (not real) number
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