Solve a^2 2a^5a^2-a^2

Question

Simplify the expression

2 a^{9} - a^{2}

Evaluate

a^{2} \times 2 a^{5} \times a^{2} - a^{2}

Solution

More Steps

Evaluate

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

Multiply the terms with the same base by adding their exponents

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

Add the numbers

a^{9} \times 2

Use the commutative property to reorder the terms

2 a^{9}

2 a^{9} - a^{2}

Show Solution

Factor the expression

a^{2} (2 a^{7} - 1)

Evaluate

a^{2} \times 2 a^{5} \times a^{2} - a^{2}

Multiply

More Steps

Evaluate

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

Multiply the terms with the same base by adding their exponents

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

Add the numbers

a^{9} \times 2

Use the commutative property to reorder the terms

2 a^{9}

2 a^{9} - a^{2}

Rewrite the expression

a^{2} \times 2 a^{7} - a^{2}

Solution

a^{2} (2 a^{7} - 1)

Show Solution

Find the roots

a_{1} = 0, a_{2} = \frac{7 64}{2}

Alternative Form

a_{1} = 0, a_{2} \approx 0.905724

Evaluate

a^{2} \times 2 a^{5} \times a^{2} - a^{2}

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

a^{2} \times 2 a^{5} \times a^{2} - a^{2} = 0

Multiply

More Steps

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

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

Add the numbers

a^{9} \times 2

Use the commutative property to reorder the terms

2 a^{9}

2 a^{9} - a^{2} = 0

Factor the expression

a^{2} (2 a^{7} - 1) = 0

Separate the equation into 2 possible cases

a^{2} = 0 2 a^{7} - 1 = 0

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

a = 0 2 a^{7} - 1 = 0

Solve the equation

More Steps

Evaluate

2 a^{7} - 1 = 0

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

2 a^{7} = 0 + 1

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

2 a^{7} = 1

Divide both sides

\frac{2 a ^{7}}{2} = \frac{1}{2}

Divide the numbers

a^{7} = \frac{1}{2}

Take the 7 -th root on both sides of the equation

7 a^{7} = 7 \frac{1}{2}

Calculate

a = 7 \frac{1}{2}

Simplify the root

More Steps

Evaluate

7 \frac{1}{2}

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

\frac{7 1}{7 2}

Simplify the radical expression

\frac{1}{7 2}

Multiply by the Conjugate

\frac{7 2 ^{6}}{7 2 \times 7 2 ^{6}}

Simplify

\frac{7 64}{7 2 \times 7 2 ^{6}}

Multiply the numbers

\frac{7 64}{2}

a = \frac{7 64}{2}

a = 0 a = \frac{7 64}{2}

Solution

a_{1} = 0, a_{2} = \frac{7 64}{2}

Alternative Form

a_{1} = 0, a_{2} \approx 0.905724

Show Solution