What is the answer to 4x^{2/3}+21x^{1/3}+27=0 ?

The answer to 4x^{2/3}+21x^{1/3}+27=0 is x=-729/64 ,x=-27

Solve for x: 4x^{2/3}+21x^{1/3}+27=0

The solution is x=-729/64 ,x=-27

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4 x^{\frac{2}{3}} + 21 x^{\frac{1}{3}} + 27 = 0

x = - \frac{729}{64}, x = - 27

Decimal Notation

x = - 11.390625, x = - 27

Solution steps

4 x^{\frac{2}{3}} + 21 x^{\frac{1}{3}} + 27 = 0

Use the following exponent property

: a^{\frac{n}{m}} = (a^{\frac{1}{m}})^{n}

x^{\frac{2}{3}} = (x^{\frac{1}{3}})^{2}

4 (x^{\frac{1}{3}})^{2} + 21 x^{\frac{1}{3}} + 27 = 0

Rewrite the equation with

x^{\frac{1}{3}} = u

4 u^{2} + 21 u + 27 = 0

Solve

4 u^{2} + 21 u + 27 = 0 : u = - \frac{9}{4}, u = - 3

u = - \frac{9}{4}, u = - 3

Substitute back

u = x^{\frac{1}{3}},

solve for

x

Solve

x^{\frac{1}{3}} = - \frac{9}{4} : x = - \frac{729}{64}

Solve

x^{\frac{1}{3}} = - 3 : x = - 27

x = - \frac{729}{64}, x = - 27

Verify Solutions:

x = - \frac{729}{64}

True

, x = - 27

True

The solutions are

x = - \frac{729}{64}, x = - 27

x + 2 + x - 7 = 9

x, r + s - 2 t = 2 x + y

\frac{1}{( 1 + x ^{2} )} = \frac{1}{( 2 )}

4 x^{3} - 3 x^{2.5} - 3 x + 9 = 15

x + x^{\frac{1}{2}} = 20

What is the answer to 4x^{2/3}+21x^{1/3}+27=0 ?
The answer to 4x^{2/3}+21x^{1/3}+27=0 is x=-729/64 ,x=-27
Solve for x: 4x^{2/3}+21x^{1/3}+27=0
The solution is x=-729/64 ,x=-27