Solve 28/x^4=11 - ScanMath

Question

Solve the equation

x_{1} = - \frac{4 37268}{11}, x_{2} = \frac{4 37268}{11}

Alternative Form

x_{1} \approx - 1.26311, x_{2} \approx 1.26311

Evaluate

\frac{28}{x ^{4}} = 11

Find the domain

More Steps

Evaluate

x^{4} \neq = 0

The only way a power can not be 0 is when the base not equals 0

x \neq = 0

\frac{28}{x ^{4}} = 11, x \neq = 0

Cross multiply

28 = x^{4} \times 11

Simplify the equation

28 = 11 x^{4}

Swap the sides of the equation

11 x^{4} = 28

Divide both sides

\frac{11 x ^{4}}{11} = \frac{28}{11}

Divide the numbers

x^{4} = \frac{28}{11}

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

x = \pm 4 \frac{28}{11}

Simplify the expression

More Steps

Evaluate

4 \frac{28}{11}

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

\frac{4 28}{4 11}

Multiply by the Conjugate

\frac{4 28 \times 4 1 1 ^{3}}{4 11 \times 4 1 1 ^{3}}

Simplify

\frac{4 28 \times 4 1331}{4 11 \times 4 1 1 ^{3}}

Multiply the numbers

More Steps

Evaluate

428 \times 41331

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

4 28 \times 1331

Calculate the product

437268

\frac{4 37268}{4 11 \times 4 1 1 ^{3}}

Multiply the numbers

More Steps

Evaluate

411 \times 4 1 1^{3}

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

4 11 \times 1 1^{3}

Calculate the product

4 1 1^{4}

Reduce the index of the radical and exponent with 4

11

\frac{4 37268}{11}

x = \pm \frac{4 37268}{11}

Separate the equation into 2 possible cases

x = \frac{4 37268}{11} x = - \frac{4 37268}{11}

Check if the solution is in the defined range

x = \frac{4 37268}{11} x = - \frac{4 37268}{11}, x \neq = 0

Find the intersection of the solution and the defined range

x = \frac{4 37268}{11} x = - \frac{4 37268}{11}

Solution

x_{1} = - \frac{4 37268}{11}, x_{2} = \frac{4 37268}{11}

Alternative Form

x_{1} \approx - 1.26311, x_{2} \approx 1.26311

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