Solve 21476x^(2)-2e^6x^5e 10

Question

Simplify the expression

21476 x^{2} - 20 e^{7} x^{5}

Evaluate

21476 x^{2} - 2 e^{6} x^{5} e \times 10

Solution

More Steps

Evaluate

2 e^{6} x^{5} e \times 10

Multiply the terms

20 e^{6} x^{5} e

Multiply the terms with the same base by adding their exponents

20 e^{6 + 1} x^{5}

Add the numbers

20 e^{7} x^{5}

21476 x^{2} - 20 e^{7} x^{5}

Show Solution

Factor the expression

4 x^{2} (5369 - 5 e^{7} x^{3})

Evaluate

21476 x^{2} - 2 e^{6} x^{5} e \times 10

Multiply

More Steps

Evaluate

2 e^{6} x^{5} e \times 10

Multiply the terms

20 e^{6} x^{5} e

Multiply the terms with the same base by adding their exponents

20 e^{6 + 1} x^{5}

Add the numbers

20 e^{7} x^{5}

21476 x^{2} - 20 e^{7} x^{5}

Rewrite the expression

4 x^{2} \times 5369 - 4 x^{2} \times 5 e^{7} x^{3}

Solution

4 x^{2} (5369 - 5 e^{7} x^{3})

Show Solution

Find the roots

x_{1} = 0, x_{2} = \frac{3 134225 e ^{2}}{5 e ^{3}}

Alternative Form

x_{1} = 0, x_{2} \approx 0.993011

Evaluate

21476 x^{2} - 2 e^{6} x^{5} e \times 10

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

21476 x^{2} - 2 e^{6} x^{5} e \times 10 = 0

Multiply

More Steps

Multiply the terms

2 e^{6} x^{5} e \times 10

Multiply the terms

20 e^{6} x^{5} e

Multiply the terms with the same base by adding their exponents

20 e^{6 + 1} x^{5}

Add the numbers

20 e^{7} x^{5}

21476 x^{2} - 20 e^{7} x^{5} = 0

Factor the expression

4 x^{2} (5369 - 5 e^{7} x^{3}) = 0

Divide both sides

x^{2} (5369 - 5 e^{7} x^{3}) = 0

Separate the equation into 2 possible cases

x^{2} = 0 5369 - 5 e^{7} x^{3} = 0

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

x = 0 5369 - 5 e^{7} x^{3} = 0

Solve the equation

More Steps

Evaluate

5369 - 5 e^{7} x^{3} = 0

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

- 5 e^{7} x^{3} = 0 - 5369

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

- 5 e^{7} x^{3} = - 5369

Change the signs on both sides of the equation

5 e^{7} x^{3} = 5369

Divide both sides

\frac{5 e ^{7} x ^{3}}{5 e ^{7}} = \frac{5369}{5 e ^{7}}

Divide the numbers

x^{3} = \frac{5369}{5 e ^{7}}

Take the 3 -th root on both sides of the equation

3 x^{3} = 3 \frac{5369}{5 e ^{7}}

Calculate

x = 3 \frac{5369}{5 e ^{7}}

Simplify the root

More Steps

Evaluate

3 \frac{5369}{5 e ^{7}}

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

\frac{3 5369}{3 5 e ^{7}}

Simplify the radical expression

\frac{3 5369}{e ^{2} 3 5 e}

Multiply by the Conjugate

\frac{3 5369 \times 3 5 ^{2} e ^{2}}{e ^{2} 3 5 e \times 3 5 ^{2} e ^{2}}

Multiply the numbers

\frac{3 134225 e ^{2}}{e ^{2} 3 5 e \times 3 5 ^{2} e ^{2}}

Multiply the numbers

\frac{3 134225 e ^{2}}{5 e ^{3}}

x = \frac{3 134225 e ^{2}}{5 e ^{3}}

x = 0 x = \frac{3 134225 e ^{2}}{5 e ^{3}}

Solution

x_{1} = 0, x_{2} = \frac{3 134225 e ^{2}}{5 e ^{3}}

Alternative Form

x_{1} = 0, x_{2} \approx 0.993011

Show Solution