Solve 10x^4-4 - ScanMath

Question

Factor the expression

2 (5 x^{4} - 2)

Evaluate

10 x^{4} - 4

Solution

2 (5 x^{4} - 2)

Show Solution

x_{1} = - \frac{4 250}{5}, x_{2} = \frac{4 250}{5}

Alternative Form

x_{1} \approx - 0.795271, x_{2} \approx 0.795271

Evaluate

10 x^{4} - 4

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

10 x^{4} - 4 = 0

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

10 x^{4} = 0 + 4

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

10 x^{4} = 4

Divide both sides

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

Divide the numbers

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

Cancel out the common factor 2

x^{4} = \frac{2}{5}

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

x = \pm 4 \frac{2}{5}

Simplify the expression

More Steps

Evaluate

4 \frac{2}{5}

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

\frac{4 2}{4 5}

Multiply by the Conjugate

\frac{4 2 \times 4 5 ^{3}}{4 5 \times 4 5 ^{3}}

Simplify

\frac{4 2 \times 4 125}{4 5 \times 4 5 ^{3}}

Multiply the numbers

More Steps

Evaluate

42 \times 4125

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

4 2 \times 125

Calculate the product

4250

\frac{4 250}{4 5 \times 4 5 ^{3}}

Multiply the numbers

More Steps

Evaluate

45 \times 4 5^{3}

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

4 5 \times 5^{3}

Calculate the product

4 5^{4}

Reduce the index of the radical and exponent with 4

5

\frac{4 250}{5}

x = \pm \frac{4 250}{5}

Separate the equation into 2 possible cases

x = \frac{4 250}{5} x = - \frac{4 250}{5}

Solution

x_{1} = - \frac{4 250}{5}, x_{2} = \frac{4 250}{5}

Alternative Form

x_{1} \approx - 0.795271, x_{2} \approx 0.795271

Show Solution