Solve 3x^2-6x^5 x^2 4

Question

Simplify the expression

3 x^{2} - 24 x^{7}

Evaluate

3 x^{2} - 6 x^{5} \times x^{2} \times 4

Solution

More Steps

Evaluate

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

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

24 x^{5 + 2}

Add the numbers

24 x^{7}

3 x^{2} - 24 x^{7}

Show Solution

Factor the expression

3 x^{2} (1 - 8 x^{5})

Evaluate

3 x^{2} - 6 x^{5} \times x^{2} \times 4

Multiply

More Steps

Evaluate

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

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

24 x^{5 + 2}

Add the numbers

24 x^{7}

3 x^{2} - 24 x^{7}

Rewrite the expression

3 x^{2} - 3 x^{2} \times 8 x^{5}

Solution

3 x^{2} (1 - 8 x^{5})

Show Solution

Find the roots

x_{1} = 0, x_{2} = \frac{5 4}{2}

Alternative Form

x_{1} = 0, x_{2} \approx 0.659754

Evaluate

3 x^{2} - 6 x^{5} \times x^{2} \times 4

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

3 x^{2} - 6 x^{5} \times x^{2} \times 4 = 0

Multiply

More Steps

Multiply the terms

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

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

24 x^{5 + 2}

Add the numbers

24 x^{7}

3 x^{2} - 24 x^{7} = 0

Factor the expression

3 x^{2} (1 - 8 x^{5}) = 0

Divide both sides

x^{2} (1 - 8 x^{5}) = 0

Separate the equation into 2 possible cases

x^{2} = 0 1 - 8 x^{5} = 0

The only way a power can be 0 is when the base equals 0

x = 0 1 - 8 x^{5} = 0

Solve the equation

More Steps

Evaluate

1 - 8 x^{5} = 0

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

- 8 x^{5} = 0 - 1

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

- 8 x^{5} = - 1

Change the signs on both sides of the equation

8 x^{5} = 1

Divide both sides

\frac{8 x ^{5}}{8} = \frac{1}{8}

Divide the numbers

x^{5} = \frac{1}{8}

Take the 5 -th root on both sides of the equation

5 x^{5} = 5 \frac{1}{8}

Calculate

x = 5 \frac{1}{8}

Simplify the root

More Steps

Evaluate

5 \frac{1}{8}

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

\frac{5 1}{5 8}

Simplify the radical expression

\frac{1}{5 8}

Multiply by the Conjugate

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

Simplify

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

Multiply the numbers

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

Reduce the fraction

\frac{5 4}{2}

x = \frac{5 4}{2}

x = 0 x = \frac{5 4}{2}

Solution

x_{1} = 0, x_{2} = \frac{5 4}{2}

Alternative Form

x_{1} = 0, x_{2} \approx 0.659754

Show Solution