Solve 6x^48x^6=180

Question

Solve the equation

x_{1} = - \frac{10 3840}{2}, x_{2} = \frac{10 3840}{2}

Alternative Form

x_{1} \approx - 1.141309, x_{2} \approx 1.141309

Evaluate

6 x^{4} \times 8 x^{6} = 180

Multiply

More Steps

Evaluate

6 x^{4} \times 8 x^{6}

Multiply the terms

48 x^{4} \times x^{6}

Multiply the terms with the same base by adding their exponents

48 x^{4 + 6}

Add the numbers

48 x^{10}

48 x^{10} = 180

Divide both sides

\frac{48 x ^{10}}{48} = \frac{180}{48}

Divide the numbers

x^{10} = \frac{180}{48}

Cancel out the common factor 12

x^{10} = \frac{15}{4}

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

x = \pm 10 \frac{15}{4}

Simplify the expression

More Steps

Evaluate

10 \frac{15}{4}

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

\frac{10 15}{10 4}

Simplify the radical expression

More Steps

Evaluate

104

Write the number in exponential form with the base of 2

10 2^{2}

Reduce the index of the radical and exponent with 2

52

\frac{10 15}{5 2}

Multiply by the Conjugate

\frac{10 15 \times 5 2 ^{4}}{5 2 \times 5 2 ^{4}}

Simplify

\frac{10 15 \times 5 16}{5 2 \times 5 2 ^{4}}

Multiply the numbers

More Steps

Evaluate

1015 \times 516

Use n a = mn a^{m} to expand the expression

1015 \times 10 1 6^{2}

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

10 15 \times 1 6^{2}

Calculate the product

103840

\frac{10 3840}{5 2 \times 5 2 ^{4}}

Multiply the numbers

More Steps

Evaluate

52 \times 5 2^{4}

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

5 2 \times 2^{4}

Calculate the product

5 2^{5}

Reduce the index of the radical and exponent with 5

2

\frac{10 3840}{2}

x = \pm \frac{10 3840}{2}

Separate the equation into 2 possible cases

x = \frac{10 3840}{2} x = - \frac{10 3840}{2}

Solution

x_{1} = - \frac{10 3840}{2}, x_{2} = \frac{10 3840}{2}

Alternative Form

x_{1} \approx - 1.141309, x_{2} \approx 1.141309

Show Solution