Solve x^4 5x^2 -4

Question

Simplify the expression

5 x^{6} - 4

Evaluate

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

Solution

More Steps

Evaluate

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

Multiply the terms with the same base by adding their exponents

x^{4 + 2} \times 5

Add the numbers

x^{6} \times 5

Use the commutative property to reorder the terms

5 x^{6}

5 x^{6} - 4

Show Solution

x_{1} = - \frac{6 12500}{5}, x_{2} = \frac{6 12500}{5}

Alternative Form

x_{1} \approx - 0.963492, x_{2} \approx 0.963492

Evaluate

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

To find the roots of the expression,set the expression equal to 0

x^{4} \times 5 x^{2} - 4 = 0

Multiply

More Steps

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

x^{4 + 2} \times 5

Add the numbers

x^{6} \times 5

Use the commutative property to reorder the terms

5 x^{6}

5 x^{6} - 4 = 0

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

5 x^{6} = 0 + 4

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

5 x^{6} = 4

Divide both sides

\frac{5 x ^{6}}{5} = \frac{4}{5}

Divide the numbers

x^{6} = \frac{4}{5}

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

x = \pm 6 \frac{4}{5}

Simplify the expression

More Steps

Evaluate

6 \frac{4}{5}

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

\frac{6 4}{6 5}

Simplify the radical expression

More Steps

Evaluate

64

Write the number in exponential form with the base of 2

6 2^{2}

Reduce the index of the radical and exponent with 2

32

\frac{3 2}{6 5}

Multiply by the Conjugate

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

Simplify

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

Multiply the numbers

More Steps

Evaluate

32 \times 63125

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

6 2^{2} \times 63125

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

6 2^{2} \times 3125

Calculate the product

612500

\frac{6 12500}{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{6 12500}{5}

x = \pm \frac{6 12500}{5}

Separate the equation into 2 possible cases

x = \frac{6 12500}{5} x = - \frac{6 12500}{5}

Solution

x_{1} = - \frac{6 12500}{5}, x_{2} = \frac{6 12500}{5}

Alternative Form

x_{1} \approx - 0.963492, x_{2} \approx 0.963492

Show Solution