x3−216=0

Add 216

to both sides of the equation.

x3=216

Move 216

to the LEFT SIDE of the equation by subtracting it from both sides.

x3−216=0

Factor the left side of the equation.

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Rewrite 216

as 63

.

x3−63=0

Since both TERMS are perfect cubes, factor using the difference of cubes formula, a3−b3=(a−b)(a2+ab+b2)

where a=x and b=6

.

(x−6)(x2+x⋅6+62)=0

Simplify.

(x−6)(x2+6x+36)=0

SET x−6

equal to 0 and solve

Set the factor equal to 0

.

x−6=0

Add 6

to both sides of the equation.

x=6

Set x2+6x+36

equal to 0 and solve for x

Set the factor equal to

x2+6x+36=0

Use the quadratic formula to find the solutions.

−b±√b2−4(ac)2a

Substitute the values a=1

, b=6, and c=36 into the quadratic formula and solve for x

−6±√62−4⋅(1⋅36)2⋅1

Simplify

x=−3±3i√3

Simplify the expression to solve for the +

portion of the ±

x=−3+3i√3

Simplify the expression to solve for the −

portion of the ±

.

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Simplify the numerator.

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x=−6±6i√32⋅1

Multiply 2

by 1

.

x=−6±6i√32

Simplify −6±6i√32

.

x=−3±3i√3

Change the ±

to −

.

x=−3−3i√3

The final answer is the combination of both solutions.

x=−3+3i√3,−3−3i√3

The solution is the result of x−6=0

and x2+6x+36=0

.

x=6,−3+3i√3,−3−3i√3