Solve x^4-2x^3-13x^214x^24

Question

Simplify the expression

Solution

- 727 x^{4} - 2 x^{3}

Evaluate

x^{4} - 2 x^{3} - 13 x^{2} \times 14 x^{2} \times 4

Multiply

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Multiply the terms

- 13 x^{2} \times 14 x^{2} \times 4

Multiply the terms

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Evaluate

13 \times 14 \times 4

Multiply the terms

182 \times 4

Multiply the numbers

728

- 728 x^{2} \times x^{2}

Multiply the terms with the same base by adding their exponents

- 728 x^{2 + 2}

Add the numbers

- 728 x^{4}

x^{4} - 2 x^{3} - 728 x^{4}

Solution

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Evaluate

x^{4} - 728 x^{4}

Collect like terms by calculating the sum or difference of their coefficients

(1 - 728) x^{4}

Subtract the numbers

- 727 x^{4}

- 727 x^{4} - 2 x^{3}

Show Solution

Factor the expression

Factor

- x^{3} (727 x + 2)

Evaluate

x^{4} - 2 x^{3} - 13 x^{2} \times 14 x^{2} \times 4

Multiply

More Steps

Multiply the terms

13 x^{2} \times 14 x^{2} \times 4

Multiply the terms

More Steps

Evaluate

13 \times 14 \times 4

Multiply the terms

182 \times 4

Multiply the numbers

728

728 x^{2} \times x^{2}

Multiply the terms with the same base by adding their exponents

728 x^{2 + 2}

Add the numbers

728 x^{4}

x^{4} - 2 x^{3} - 728 x^{4}

Subtract the terms

More Steps

Evaluate

x^{4} - 728 x^{4}

Collect like terms by calculating the sum or difference of their coefficients

(1 - 728) x^{4}

Subtract the numbers

- 727 x^{4}

- 727 x^{4} - 2 x^{3}

Rewrite the expression

- x^{3} \times 727 x - x^{3} \times 2

Solution

- x^{3} (727 x + 2)

Show Solution

Find the roots

Find the roots of the algebra expression

x_{1} = - \frac{2}{727}, x_{2} = 0

Alternative Form

x_{1} \approx - 0.002751, x_{2} = 0

Evaluate

x^{4} - 2 x^{3} - 13 x^{2} \times 14 x^{2} \times 4

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

x^{4} - 2 x^{3} - 13 x^{2} \times 14 x^{2} \times 4 = 0

Multiply

More Steps

Multiply the terms

13 x^{2} \times 14 x^{2} \times 4

Multiply the terms

More Steps

Evaluate

13 \times 14 \times 4

Multiply the terms

182 \times 4

Multiply the numbers

728

728 x^{2} \times x^{2}

Multiply the terms with the same base by adding their exponents

728 x^{2 + 2}

Add the numbers

728 x^{4}

x^{4} - 2 x^{3} - 728 x^{4} = 0

Subtract the terms

More Steps

Simplify

x^{4} - 2 x^{3} - 728 x^{4}

Subtract the terms

More Steps

Evaluate

x^{4} - 728 x^{4}

Collect like terms by calculating the sum or difference of their coefficients

(1 - 728) x^{4}

Subtract the numbers

- 727 x^{4}

- 727 x^{4} - 2 x^{3}

- 727 x^{4} - 2 x^{3} = 0

Factor the expression

- x^{3} (727 x + 2) = 0

Divide both sides

x^{3} (727 x + 2) = 0

Separate the equation into 2 possible cases

x^{3} = 0 727 x + 2 = 0

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

x = 0 727 x + 2 = 0

Solve the equation

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Evaluate

727 x + 2 = 0

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

727 x = 0 - 2

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

727 x = - 2

Divide both sides

\frac{727 x}{727} = \frac{- 2}{727}

Divide the numbers

x = \frac{- 2}{727}

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

x = - \frac{2}{727}

x = 0 x = - \frac{2}{727}

Solution

x_{1} = - \frac{2}{727}, x_{2} = 0

Alternative Form

x_{1} \approx - 0.002751, x_{2} = 0

Show Solution

X^4 2x^3 13x^214x^24

Simplify the expression

Solution

Factor the expression

Factor

Find the roots

Find the roots of the algebra expression