Solve x^2x^45=192

Question

Solve the equation

x_{1} = - \frac{2 6 9375}{5}, x_{2} = \frac{2 6 9375}{5}

Alternative Form

x_{1} \approx - 1.836772, x_{2} \approx 1.836772

Evaluate

x^{2} \times x^{4} \times 5 = 192

Multiply

More Steps

Evaluate

x^{2} \times x^{4} \times 5

Multiply the terms with the same base by adding their exponents

x^{2 + 4} \times 5

Add the numbers

x^{6} \times 5

Use the commutative property to reorder the terms

5 x^{6}

5 x^{6} = 192

Divide both sides

\frac{5 x ^{6}}{5} = \frac{192}{5}

Divide the numbers

x^{6} = \frac{192}{5}

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

x = \pm 6 \frac{192}{5}

Simplify the expression

More Steps

Evaluate

6 \frac{192}{5}

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

\frac{6 192}{6 5}

Simplify the radical expression

More Steps

Evaluate

6192

Write the expression as a product where the root of one of the factors can be evaluated

6 64 \times 3

Write the number in exponential form with the base of 2

6 2^{6} \times 3

The root of a product is equal to the product of the roots of each factor

6 2^{6} \times 63

Reduce the index of the radical and exponent with 6

263

\frac{2 6 3}{6 5}

Multiply by the Conjugate

\frac{2 6 3 \times 6 5 ^{5}}{6 5 \times 6 5 ^{5}}

Simplify

\frac{2 6 3 \times 6 3125}{6 5 \times 6 5 ^{5}}

Multiply the numbers

More Steps

Evaluate

63 \times 63125

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

6 3 \times 3125

Calculate the product

69375

\frac{2 6 9375}{6 5 \times 6 5 ^{5}}

Multiply the numbers

More Steps

Evaluate

65 \times 6 5^{5}

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

6 5 \times 5^{5}

Calculate the product

6 5^{6}

Reduce the index of the radical and exponent with 6

5

\frac{2 6 9375}{5}

x = \pm \frac{2 6 9375}{5}

Separate the equation into 2 possible cases

x = \frac{2 6 9375}{5} x = - \frac{2 6 9375}{5}

Solution

x_{1} = - \frac{2 6 9375}{5}, x_{2} = \frac{2 6 9375}{5}

Alternative Form

x_{1} \approx - 1.836772, x_{2} \approx 1.836772

Show Solution