Solve 3x-52x^5 - Socratic AI (ScanMath)

Pergunta

Factor the expression

x (3 - 52 x^{4})

Evaluate

3 x - 52 x^{5}

Rewrite the expression

x \times 3 - x \times 52 x^{4}

Solução

x (3 - 52 x^{4})

Mostrar solução

x_{1} = - \frac{4 3 \times 5 2 ^{3}}{52}, x_{2} = 0, x_{3} = \frac{4 3 \times 5 2 ^{3}}{52}

Alternative Form

x_{1} \approx - 0.490094, x_{2} = 0, x_{3} \approx 0.490094

Evaluate

3 x - 52 x^{5}

To find the roots of the expression,set the expression equal to 0

3 x - 52 x^{5} = 0

Factor the expression

x (3 - 52 x^{4}) = 0

Separate the equation into 2 possible cases

x = 0 3 - 52 x^{4} = 0

Solve the equation

Mais Passos

Evaluate

3 - 52 x^{4} = 0

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

- 52 x^{4} = 0 - 3

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

- 52 x^{4} = - 3

Change the signs on both sides of the equation

52 x^{4} = 3

Divide both sides

\frac{52 x ^{4}}{52} = \frac{3}{52}

Divide the numbers

x^{4} = \frac{3}{52}

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm 4 \frac{3}{52}

Simplify the expression

Mais Passos

Evaluate

4 \frac{3}{52}

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

\frac{4 3}{4 52}

Multiply by the Conjugate

\frac{4 3 \times 4 5 2 ^{3}}{4 52 \times 4 5 2 ^{3}}

The product of roots with the same index is equal to the root of the product

\frac{4 3 \times 5 2 ^{3}}{4 52 \times 4 5 2 ^{3}}

Multiply the numbers

\frac{4 3 \times 5 2 ^{3}}{52}

x = \pm \frac{4 3 \times 5 2 ^{3}}{52}

Separate the equation into 2 possible cases

x = \frac{4 3 \times 5 2 ^{3}}{52} x = - \frac{4 3 \times 5 2 ^{3}}{52}

x = 0 x = \frac{4 3 \times 5 2 ^{3}}{52} x = - \frac{4 3 \times 5 2 ^{3}}{52}

Solução

x_{1} = - \frac{4 3 \times 5 2 ^{3}}{52}, x_{2} = 0, x_{3} = \frac{4 3 \times 5 2 ^{3}}{52}

Alternative Form

x_{1} \approx - 0.490094, x_{2} = 0, x_{3} \approx 0.490094

Mostrar solução