Solve 5k^2-3k^2 8k^2 9k-8

Question

Simplify the expression

5 k^{2} - 216 k^{5} - 8

Evaluate

5 k^{2} - 3 k^{2} \times 8 k^{2} \times 9 k - 8

Solution

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Evaluate

- 3 k^{2} \times 8 k^{2} \times 9 k

Multiply the terms

More Steps

Evaluate

3 \times 8 \times 9

Multiply the terms

24 \times 9

Multiply the numbers

216

- 216 k^{2} \times k^{2} \times k

Multiply the terms with the same base by adding their exponents

- 216 k^{2 + 2 + 1}

Add the numbers

- 216 k^{5}

5 k^{2} - 216 k^{5} - 8

Show Solution

Factor the expression

- (2 k + 1) (108 k^{4} - 54 k^{3} + 27 k^{2} - 16 k + 8)

Evaluate

5 k^{2} - 3 k^{2} \times 8 k^{2} \times 9 k - 8

Multiply

More Steps

Evaluate

3 k^{2} \times 8 k^{2} \times 9 k

Multiply the terms

More Steps

Evaluate

3 \times 8 \times 9

Multiply the terms

24 \times 9

Multiply the numbers

216

216 k^{2} \times k^{2} \times k

Multiply the terms with the same base by adding their exponents

216 k^{2 + 2 + 1}

Add the numbers

216 k^{5}

5 k^{2} - 216 k^{5} - 8

Calculate

- 216 k^{5} + 108 k^{4} - 54 k^{3} + 32 k^{2} - 16 k - 108 k^{4} + 54 k^{3} - 27 k^{2} + 16 k - 8

Rewrite the expression

- 2 k \times 108 k^{4} + 2 k \times 54 k^{3} - 2 k \times 27 k^{2} + 2 k \times 16 k - 2 k \times 8 - 108 k^{4} + 54 k^{3} - 27 k^{2} + 16 k - 8

Factor out - 2 k from the expression

- 2 k (108 k^{4} - 54 k^{3} + 27 k^{2} - 16 k + 8) - 108 k^{4} + 54 k^{3} - 27 k^{2} + 16 k - 8

Factor out - 1 from the expression

- 2 k (108 k^{4} - 54 k^{3} + 27 k^{2} - 16 k + 8) - (108 k^{4} - 54 k^{3} + 27 k^{2} - 16 k + 8)

Factor out 108 k^{4} - 54 k^{3} + 27 k^{2} - 16 k + 8 from the expression

(- 2 k - 1) (108 k^{4} - 54 k^{3} + 27 k^{2} - 16 k + 8)

Solution

- (2 k + 1) (108 k^{4} - 54 k^{3} + 27 k^{2} - 16 k + 8)

Show Solution

Find the roots

k = - \frac{1}{2}

Alternative Form

k = - 0.5

Evaluate

5 k^{2} - 3 k^{2} \times 8 k^{2} \times 9 k - 8

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

5 k^{2} - 3 k^{2} \times 8 k^{2} \times 9 k - 8 = 0

Multiply

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Multiply the terms

3 k^{2} \times 8 k^{2} \times 9 k

Multiply the terms

More Steps

Evaluate

3 \times 8 \times 9

Multiply the terms

24 \times 9

Multiply the numbers

216

216 k^{2} \times k^{2} \times k

Multiply the terms with the same base by adding their exponents

216 k^{2 + 2 + 1}

Add the numbers

216 k^{5}

5 k^{2} - 216 k^{5} - 8 = 0

Factor the expression

(- 2 k - 1) (108 k^{4} - 54 k^{3} + 27 k^{2} - 16 k + 8) = 0

Separate the equation into 2 possible cases

- 2 k - 1 = 0 108 k^{4} - 54 k^{3} + 27 k^{2} - 16 k + 8 = 0

Solve the equation

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Evaluate

- 2 k - 1 = 0

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

- 2 k = 0 + 1

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

- 2 k = 1

Change the signs on both sides of the equation

2 k = - 1

Divide both sides

\frac{2 k}{2} = \frac{- 1}{2}

Divide the numbers

k = \frac{- 1}{2}

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

k = - \frac{1}{2}

k = - \frac{1}{2} 108 k^{4} - 54 k^{3} + 27 k^{2} - 16 k + 8 = 0

Solve the equation

k = - \frac{1}{2} k \in / R

Solution

k = - \frac{1}{2}

Alternative Form

k = - 0.5

Show Solution