Finish this equation

**helvenmarn** · June 18th 2012, 01:01 PM

$3(x-3)^3=375$
$(x-3)^3=125$
$x^3-9x^2+27x-9=125$
$x^3-9x^2+27x-134=0$

Not sure where to go from here

**emakarov** · June 18th 2012, 01:04 PM

y³ = 125 is equivalent to y = 5.

**helvenmarn** · June 18th 2012, 01:20 PM

Sorry? What y? I need to find the value of x. The answer is supposedly 8.

**Plato** · June 18th 2012, 01:22 PM

Originally Posted by helvenmarn

Sorry? What y? I need to find the value of x. The answer is supposedly 8.

$(8-3)^3=125$

**simamura** · June 18th 2012, 01:22 PM

$(x-3)^3=125$
Since $125=5^3$ then $(x-3)^3=5^3$ .
From this we have that x-3=5 or x=8

**helvenmarn** · June 18th 2012, 01:31 PM

Ah thanks

**richard1234** · June 18th 2012, 02:41 PM

No need to expand.

From $(x-3)^3 = 125$ , we get $x-3 = 5 \Rightarrow x = 8$ . There are also two roots in the complex plane, $x = 3 + 5e^{\frac{2\pi i}{3}}$ and $x = 3 + 5e^{\frac{4\pi i}{3}}$

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