SOLUTION: x3 − 125 = 0 find all solutions of the equation

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Question 666718: x3 − 125 = 0 find all solutions of the equation
Found 2 solutions by ewatrrr, MathLover1:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

x%5E3+-+125+=+0

    x^3 = 125

    x = 5     || As 5%2A5%2A5+=+125

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E3-125+=+0+
x%5E3-5%5E3+=+0+....use the difference of cubes rule a%5E3+%96+b%5E3+=+%28a+%96+b%29%28a%5E2+%2B+ab+%2B+b%5E2%29
%28x-5%29%28x%5E2%2B5x%2B25%29+=+0+
%28x-5%29%28x%5E2%2B5x%2B25%29+=+0+
if %28x-5%29=+0+...=>...x=5......one real solution
if %28x%5E2%2B5x%2B25%29=+0...=>....use quadratic formula to fine to remaining solutions
%28x%5E2%2B5x%2B25%29=+0
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-5+%2B-+sqrt%28+5%5E2-4%2A1%2A25+%29%29%2F%282%2A1%29+
x+=+%28-5+%2B-+sqrt%28+25-100+%29%29%2F2+
x+=+%28-5+%2B-+sqrt%28+-75+%29%29%2F2+
x+=+%28-5+%2B-+8.66%2Ai%29%2F2+
solutions
x+=+-5%2F2+%2B+8.66%2Ai%2F2+
x+=+-2.5+%2B+4.33%2Ai+
and
x+=+-5%2F2+-8.66%2Ai%2F2+
x+=+-2.5+-4.33%2Ai+
these two are complex solutions

+graph%28+600%2C+600%2C+-10%2C+10%2C+-200%2C+130%2C+x%5E3-125%29+