Solve x^238x^22=180

Question

Solve the equation

x_{1} = - \frac{4 308655}{19}, x_{2} = \frac{4 308655}{19}

Alternative Form

x_{1} \approx - 1.240551, x_{2} \approx 1.240551

Evaluate

x^{2} \times 38 x^{2} \times 2 = 180

Multiply

More Steps

Evaluate

x^{2} \times 38 x^{2} \times 2

Multiply the terms with the same base by adding their exponents

x^{2 + 2} \times 38 \times 2

Add the numbers

x^{4} \times 38 \times 2

Multiply the terms

x^{4} \times 76

Use the commutative property to reorder the terms

76 x^{4}

76 x^{4} = 180

Divide both sides

\frac{76 x ^{4}}{76} = \frac{180}{76}

Divide the numbers

x^{4} = \frac{180}{76}

Cancel out the common factor 4

x^{4} = \frac{45}{19}

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

x = \pm 4 \frac{45}{19}

Simplify the expression

More Steps

Evaluate

4 \frac{45}{19}

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

\frac{4 45}{4 19}

Multiply by the Conjugate

\frac{4 45 \times 4 1 9 ^{3}}{4 19 \times 4 1 9 ^{3}}

Simplify

\frac{4 45 \times 4 6859}{4 19 \times 4 1 9 ^{3}}

Multiply the numbers

More Steps

Evaluate

445 \times 46859

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

4 45 \times 6859

Calculate the product

4308655

\frac{4 308655}{4 19 \times 4 1 9 ^{3}}

Multiply the numbers

More Steps

Evaluate

419 \times 4 1 9^{3}

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

4 19 \times 1 9^{3}

Calculate the product

4 1 9^{4}

Reduce the index of the radical and exponent with 4

19

\frac{4 308655}{19}

x = \pm \frac{4 308655}{19}

Separate the equation into 2 possible cases

x = \frac{4 308655}{19} x = - \frac{4 308655}{19}

Solution

x_{1} = - \frac{4 308655}{19}, x_{2} = \frac{4 308655}{19}

Alternative Form

x_{1} \approx - 1.240551, x_{2} \approx 1.240551

Show Solution