How do you solve $5^3=(x+2)^3$ ?

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Answer 1 · 2015-09-10T02:07:28

$x = 3$

$5^3 = (x + 2)^3$ => rewrite as:

$(x + 2)^3 - 5^3 = 0$ => factor by the difference of cubes formula:

$[(x + 2) - 5][(x + 2)^2+ 5(x + 2)+25]=0$ => simplify:

$(x - 3)(x^2 + 9x + 39)=0$ => equate each bracket to zero:

$x - 3 = 0 => x = 3$

$x^2 + 9x + 39 = 0$

Discriminant $= b^2 - 4ac = 81 - 156 = -75<0$

Since the discriminant is negative the quadratic has no real solutions therefore the only valid solution is:

$x = 3$

How do you solve 5^3=(x+2)^3 5^3=(x+2)^3?