27x^3+216=0
x^4+x^3-x=1
x^4+x^3-x=1
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27x^3+216=0
first take a 3rd root of the terms
3x * 3x * 3x + 6 * 6 * 6 = 0
now it is easy to see that 3x + 6 = 0
move the 6 to the other side (don't forget to change the sign)
so 3x = -6
divide by three and you have
x = -2
check solution
27 *(-2)^3 + 216=0
27 * -8 +216 =0
-216+216=0
0=0 check
2nd equation:
x^4+x^3-x=1
rewrite the equation like this:
x^3(x+1)-x=1
then move the x to the other side (don't forget to change the sign)
x^3(x+1)=x+1
divide both sides by (x+1) to obtain
X^3 = 1
take a third root of both sides to solve
x=1
check solution
1^4 + 1^3 -1 = 1
1 + 1 -1 =1
1 = 1 check
first take a 3rd root of the terms
3x * 3x * 3x + 6 * 6 * 6 = 0
now it is easy to see that 3x + 6 = 0
move the 6 to the other side (don't forget to change the sign)
so 3x = -6
divide by three and you have
x = -2
check solution
27 *(-2)^3 + 216=0
27 * -8 +216 =0
-216+216=0
0=0 check
2nd equation:
x^4+x^3-x=1
rewrite the equation like this:
x^3(x+1)-x=1
then move the x to the other side (don't forget to change the sign)
x^3(x+1)=x+1
divide both sides by (x+1) to obtain
X^3 = 1
take a third root of both sides to solve
x=1
check solution
1^4 + 1^3 -1 = 1
1 + 1 -1 =1
1 = 1 check
-
27x^3+216=0
subtract 216 from both sides: 27x^3 = -216
divided both sides by 27: x^3 = -8
take the cube root of both sides: x = -2
x^4+x^3-x=1
use the quadratic equation --> x = + or - 1
subtract 216 from both sides: 27x^3 = -216
divided both sides by 27: x^3 = -8
take the cube root of both sides: x = -2
x^4+x^3-x=1
use the quadratic equation --> x = + or - 1