Solve 4x^4-5 25/5

Question

Simplify the expression

4 x^{4} - 10

Evaluate

4 x^{4} - 5 \frac{25}{5}

Covert the mixed number to an improper fraction

More Steps

Convert the expressions

5 \frac{25}{5}

Multiply the denominator of the fraction by the whole number and add the numerator of the fraction

\frac{5 \times 5 + 25}{5}

Multiply the terms

\frac{25 + 25}{5}

Add the terms

\frac{50}{5}

4 x^{4} - \frac{50}{5}

Solution

4 x^{4} - 10

Show Solution

Factor the expression

2 (2 x^{4} - 5)

Evaluate

4 x^{4} - 5 \frac{25}{5}

Covert the mixed number to an improper fraction

More Steps

Convert the expressions

5 \frac{25}{5}

Multiply the denominator of the fraction by the whole number and add the numerator of the fraction

\frac{5 \times 5 + 25}{5}

Multiply the terms

\frac{25 + 25}{5}

Add the terms

\frac{50}{5}

4 x^{4} - \frac{50}{5}

Evaluate

4 x^{4} - 10

Solution

2 (2 x^{4} - 5)

Show Solution

Find the roots

x_{1} = - \frac{4 40}{2}, x_{2} = \frac{4 40}{2}

Alternative Form

x_{1} \approx - 1.257433, x_{2} \approx 1.257433

Evaluate

4 x^{4} - 5 \frac{25}{5}

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

4 x^{4} - 5 \frac{25}{5} = 0

Covert the mixed number to an improper fraction

More Steps

Convert the expressions

5 \frac{25}{5}

Multiply the denominator of the fraction by the whole number and add the numerator of the fraction

\frac{5 \times 5 + 25}{5}

Multiply the terms

\frac{25 + 25}{5}

Add the terms

\frac{50}{5}

4 x^{4} - \frac{50}{5} = 0

Calculate

4 x^{4} - 10 = 0

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

4 x^{4} = 0 + 10

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

4 x^{4} = 10

Divide both sides

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

Divide the numbers

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

Cancel out the common factor 2

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

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

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

Simplify the expression

More Steps

Evaluate

4 \frac{5}{2}

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

\frac{4 5}{4 2}

Multiply by the Conjugate

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

Simplify

\frac{4 5 \times 4 8}{4 2 \times 4 2 ^{3}}

Multiply the numbers

More Steps

Evaluate

45 \times 48

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

4 5 \times 8

Calculate the product

440

\frac{4 40}{4 2 \times 4 2 ^{3}}

Multiply the numbers

More Steps

Evaluate

42 \times 4 2^{3}

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

4 2 \times 2^{3}

Calculate the product

4 2^{4}

Reduce the index of the radical and exponent with 4

2

\frac{4 40}{2}

x = \pm \frac{4 40}{2}

Separate the equation into 2 possible cases

x = \frac{4 40}{2} x = - \frac{4 40}{2}

Solution

x_{1} = - \frac{4 40}{2}, x_{2} = \frac{4 40}{2}

Alternative Form

x_{1} \approx - 1.257433, x_{2} \approx 1.257433

Show Solution