SOLUTION: Find the solutions of the equation. (Enter your answers as a comma-separated list.) x^4 = 625

Algebra ->  Square-cubic-other-roots -> SOLUTION: Find the solutions of the equation. (Enter your answers as a comma-separated list.) x^4 = 625       Log On


   

Question 903856: Find the solutions of the equation. (Enter your answers as a comma-separated list.)
x^4 = 625
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E4+=+625

x%5E4+-+625+=+0

%28x%5E2%29%5E2+-+%2825%29%5E2+=+0

%28x%5E2+-+25%29%28x%5E2+%2B+25%29+=+0

%28x+-+5%29%28x+%2B+5%29%28x%5E2+%2B+25%29+=+0

x+-+5+=+0, x+%2B+5+=+0, x%5E2+%2B+25+=+0

x=5, x+=+-5, x+=+5i or x+=+-5i

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Side Note: solving x%5E2+%2B+25+=+0 gives x+=+5i or x+=+-5i

Further breakdown of why that is true

x%5E2+%2B+25+=+0

x%5E2+=+-25

x+=+sqrt%28-25%29 or x+=+-sqrt%28-25%29

x+=+sqrt%28-1%2A25%29 or x+=+-sqrt%28-1%2A25%29

x+=+sqrt%28-1%29%2Asqrt%2825%29 or x+=+-sqrt%28-1%29%2Asqrt%2825%29

x+=+i%2A5 or x+=+-i%2A5

x+=+5i or x+=+-5i