Solve 3a+2a^5a - ScanMath

Question

Simplify the expression

3 a + 2 a^{6}

Evaluate

3 a + 2 a^{5} \times a

Solution

More Steps

Evaluate

2 a^{5} \times a

Multiply the terms with the same base by adding their exponents

2 a^{5 + 1}

Add the numbers

2 a^{6}

3 a + 2 a^{6}

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Factor the expression

a (3 + 2 a^{5})

Evaluate

3 a + 2 a^{5} \times a

Multiply

More Steps

Evaluate

2 a^{5} \times a

Multiply the terms with the same base by adding their exponents

2 a^{5 + 1}

Add the numbers

2 a^{6}

3 a + 2 a^{6}

Rewrite the expression

a \times 3 + a \times 2 a^{5}

Solution

a (3 + 2 a^{5})

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Find the roots

a_{1} = - \frac{5 48}{2}, a_{2} = 0

Alternative Form

a_{1} \approx - 1.084472, a_{2} = 0

Evaluate

3 a + 2 a^{5} \times a

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

3 a + 2 a^{5} \times a = 0

Multiply

More Steps

Multiply the terms

2 a^{5} \times a

Multiply the terms with the same base by adding their exponents

2 a^{5 + 1}

Add the numbers

2 a^{6}

3 a + 2 a^{6} = 0

Factor the expression

a (3 + 2 a^{5}) = 0

Separate the equation into 2 possible cases

a = 0 3 + 2 a^{5} = 0

Solve the equation

More Steps

Evaluate

3 + 2 a^{5} = 0

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

2 a^{5} = 0 - 3

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

2 a^{5} = - 3

Divide both sides

\frac{2 a ^{5}}{2} = \frac{- 3}{2}

Divide the numbers

a^{5} = \frac{- 3}{2}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

a^{5} = - \frac{3}{2}

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

5 a^{5} = 5 - \frac{3}{2}

Calculate

a = 5 - \frac{3}{2}

Simplify the root

More Steps

Evaluate

5 - \frac{3}{2}

An odd root of a negative radicand is always a negative

- 5 \frac{3}{2}

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

- \frac{5 3}{5 2}

Multiply by the Conjugate

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

Simplify

\frac{- 5 3 \times 5 16}{5 2 \times 5 2 ^{4}}

Multiply the numbers

\frac{- 5 48}{5 2 \times 5 2 ^{4}}

Multiply the numbers

\frac{- 5 48}{2}

Calculate

- \frac{5 48}{2}

a = - \frac{5 48}{2}

a = 0 a = - \frac{5 48}{2}

Solution

a_{1} = - \frac{5 48}{2}, a_{2} = 0

Alternative Form

a_{1} \approx - 1.084472, a_{2} = 0

Show Solution