Solve 480-92x^4x^2=0

Question

Solve the equation

x_{1} = - \frac{6 120 \times 2 3 ^{5}}{23}, x_{2} = \frac{6 120 \times 2 3 ^{5}}{23}

Alternative Form

x_{1} \approx - 1.316969, x_{2} \approx 1.316969

Evaluate

480 - 92 x^{4} \times x^{2} = 0

Multiply

More Steps

Evaluate

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

Multiply the terms with the same base by adding their exponents

92 x^{4 + 2}

Add the numbers

92 x^{6}

480 - 92 x^{6} = 0

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

- 92 x^{6} = 0 - 480

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

- 92 x^{6} = - 480

Change the signs on both sides of the equation

92 x^{6} = 480

Divide both sides

\frac{92 x ^{6}}{92} = \frac{480}{92}

Divide the numbers

x^{6} = \frac{480}{92}

Cancel out the common factor 4

x^{6} = \frac{120}{23}

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

x = \pm 6 \frac{120}{23}

Simplify the expression

More Steps

Evaluate

6 \frac{120}{23}

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

\frac{6 120}{6 23}

Multiply by the Conjugate

\frac{6 120 \times 6 2 3 ^{5}}{6 23 \times 6 2 3 ^{5}}

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

\frac{6 120 \times 2 3 ^{5}}{6 23 \times 6 2 3 ^{5}}

Multiply the numbers

More Steps

Evaluate

623 \times 6 2 3^{5}

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

6 23 \times 2 3^{5}

Calculate the product

6 2 3^{6}

Reduce the index of the radical and exponent with 6

23

\frac{6 120 \times 2 3 ^{5}}{23}

x = \pm \frac{6 120 \times 2 3 ^{5}}{23}

Separate the equation into 2 possible cases

x = \frac{6 120 \times 2 3 ^{5}}{23} x = - \frac{6 120 \times 2 3 ^{5}}{23}

Solution

x_{1} = - \frac{6 120 \times 2 3 ^{5}}{23}, x_{2} = \frac{6 120 \times 2 3 ^{5}}{23}

Alternative Form

x_{1} \approx - 1.316969, x_{2} \approx 1.316969

Show Solution