Solve a^2 6a-16 - ScanMath

Question

Simplify the expression

6 a^{3} - 16

Evaluate

a^{2} \times 6 a - 16

Solution

More Steps

Evaluate

a^{2} \times 6 a

Multiply the terms with the same base by adding their exponents

a^{2 + 1} \times 6

Add the numbers

a^{3} \times 6

Use the commutative property to reorder the terms

6 a^{3}

6 a^{3} - 16

Show Solution

Factor the expression

2 (3 a^{3} - 8)

Evaluate

a^{2} \times 6 a - 16

Multiply

More Steps

Evaluate

a^{2} \times 6 a

Multiply the terms with the same base by adding their exponents

a^{2 + 1} \times 6

Add the numbers

a^{3} \times 6

Use the commutative property to reorder the terms

6 a^{3}

6 a^{3} - 16

Solution

2 (3 a^{3} - 8)

Show Solution

Find the roots

a = \frac{2 3 9}{3}

Alternative Form

a \approx 1.386723

Evaluate

a^{2} \times 6 a - 16

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

a^{2} \times 6 a - 16 = 0

Multiply

More Steps

Multiply the terms

a^{2} \times 6 a

Multiply the terms with the same base by adding their exponents

a^{2 + 1} \times 6

Add the numbers

a^{3} \times 6

Use the commutative property to reorder the terms

6 a^{3}

6 a^{3} - 16 = 0

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

6 a^{3} = 0 + 16

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

6 a^{3} = 16

Divide both sides

\frac{6 a ^{3}}{6} = \frac{16}{6}

Divide the numbers

a^{3} = \frac{16}{6}

Cancel out the common factor 2

a^{3} = \frac{8}{3}

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

3 a^{3} = 3 \frac{8}{3}

Calculate

a = 3 \frac{8}{3}

Solution

More Steps

Evaluate

3 \frac{8}{3}

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

\frac{3 8}{3 3}

Simplify the radical expression

More Steps

Evaluate

38

Write the number in exponential form with the base of 2

3 2^{3}

Reduce the index of the radical and exponent with 3

2

\frac{2}{3 3}

Multiply by the Conjugate

\frac{2 3 3 ^{2}}{3 3 \times 3 3 ^{2}}

Simplify

\frac{2 3 9}{3 3 \times 3 3 ^{2}}

Multiply the numbers

More Steps

Evaluate

33 \times 3 3^{2}

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

3 3 \times 3^{2}

Calculate the product

3 3^{3}

Reduce the index of the radical and exponent with 3

3

\frac{2 3 9}{3}

a = \frac{2 3 9}{3}

Alternative Form

a \approx 1.386723

Show Solution