Solve 4/3(x^6) = 2x - 3 x

Question

Solve the equation

x_{1} = - \frac{5 24}{2}, x_{2} = 0

Alternative Form

x_{1} \approx - 0.944088, x_{2} = 0

Evaluate

\frac{4}{3} x^{6} = 2 x - 3 x

Subtract the terms

More Steps

Evaluate

2 x - 3 x

Collect like terms by calculating the sum or difference of their coefficients

(2 - 3) x

Subtract the numbers

- x

\frac{4}{3} x^{6} = - x

Add or subtract both sides

\frac{4}{3} x^{6} - (- x) = 0

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

\frac{4}{3} x^{6} + x = 0

Factor the expression

x (\frac{4}{3} x^{5} + 1) = 0

Separate the equation into 2 possible cases

x = 0 \frac{4}{3} x^{5} + 1 = 0

Solve the equation

More Steps

Evaluate

\frac{4}{3} x^{5} + 1 = 0

Move the constant to the right-hand side and change its sign

\frac{4}{3} x^{5} = 0 - 1

Removing 0 doesn't change the value,so remove it from the expression

\frac{4}{3} x^{5} = - 1

Multiply by the reciprocal

\frac{4}{3} x^{5} \times \frac{3}{4} = - \frac{3}{4}

Multiply

x^{5} = - \frac{3}{4}

Take the 5 -th root on both sides of the equation

5 x^{5} = 5 - \frac{3}{4}

Calculate

x = 5 - \frac{3}{4}

Simplify the root

More Steps

Evaluate

5 - \frac{3}{4}

An odd root of a negative radicand is always a negative

- 5 \frac{3}{4}

To take a root of a fraction,take the root of the numerator and denominator separately

- \frac{5 3}{5 4}

Multiply by the Conjugate

\frac{- 5 3 \times 5 4 ^{4}}{5 4 \times 5 4 ^{4}}

Simplify

\frac{- 5 3 \times 2 5 8}{5 4 \times 5 4 ^{4}}

Multiply the numbers

\frac{- 2 5 24}{5 4 \times 5 4 ^{4}}

Multiply the numbers

\frac{- 2 5 24}{2 ^{2}}

Reduce the fraction

\frac{- 5 24}{2}

Calculate

- \frac{5 24}{2}

x = - \frac{5 24}{2}

x = 0 x = - \frac{5 24}{2}

Solution

x_{1} = - \frac{5 24}{2}, x_{2} = 0

Alternative Form

x_{1} \approx - 0.944088, x_{2} = 0

Show Solution

Solve the equation

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