Solve 2080-2r^5r^5e

Question

Simplify the expression

2080 - 2 e r^{10}

Evaluate

2080 - 2 r^{5} \times r^{5} e

Solution

More Steps

Evaluate

2 r^{5} \times r^{5} e

Multiply the terms with the same base by adding their exponents

2 r^{5 + 5} e

Add the numbers

2 r^{10} e

Multiply the numbers

2 e r^{10}

2080 - 2 e r^{10}

Show Solution

Factor the expression

2 (1040 - e r^{10})

Evaluate

2080 - 2 r^{5} \times r^{5} e

Multiply

More Steps

Evaluate

2 r^{5} \times r^{5} e

Multiply the terms with the same base by adding their exponents

2 r^{5 + 5} e

Add the numbers

2 r^{10} e

Multiply the numbers

2 e r^{10}

2080 - 2 e r^{10}

Solution

2 (1040 - e r^{10})

Show Solution

Find the roots

r_{1} = - \frac{10 1040 e ^{9}}{e}, r_{2} = \frac{10 1040 e ^{9}}{e}

Alternative Form

r_{1} \approx - 1.812483, r_{2} \approx 1.812483

Evaluate

2080 - 2 r^{5} \times r^{5} e

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

2080 - 2 r^{5} \times r^{5} e = 0

Multiply

More Steps

Multiply the terms

2 r^{5} \times r^{5} e

Multiply the terms with the same base by adding their exponents

2 r^{5 + 5} e

Add the numbers

2 r^{10} e

Multiply the numbers

2 e r^{10}

2080 - 2 e r^{10} = 0

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

- 2 e r^{10} = 0 - 2080

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

- 2 e r^{10} = - 2080

Change the signs on both sides of the equation

2 e r^{10} = 2080

Divide both sides

\frac{2 e r ^{10}}{2 e} = \frac{2080}{2 e}

Divide the numbers

r^{10} = \frac{2080}{2 e}

Cancel out the common factor 2

r^{10} = \frac{1040}{e}

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

r = \pm 10 \frac{1040}{e}

Simplify the expression

More Steps

Evaluate

10 \frac{1040}{e}

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

\frac{10 1040}{10 e}

Multiply by the Conjugate

\frac{10 1040 \times 10 e ^{9}}{10 e \times 10 e ^{9}}

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

\frac{10 1040 e ^{9}}{10 e \times 10 e ^{9}}

Multiply the numbers

More Steps

Evaluate

10 e \times 10 e^{9}

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

10 e \times e^{9}

Calculate the product

10 e^{10}

Reduce the index of the radical and exponent with 10

e

\frac{10 1040 e ^{9}}{e}

r = \pm \frac{10 1040 e ^{9}}{e}

Separate the equation into 2 possible cases

r = \frac{10 1040 e ^{9}}{e} r = - \frac{10 1040 e ^{9}}{e}

Solution

r_{1} = - \frac{10 1040 e ^{9}}{e}, r_{2} = \frac{10 1040 e ^{9}}{e}

Alternative Form

r_{1} \approx - 1.812483, r_{2} \approx 1.812483

Show Solution