Solve \frac{x^{4}-3x^{3}-7x^{2} 7x^2}{x^2}

Question

Simplify the expression

- 48 x^{2} - 3 x

Evaluate

\frac{x ^{4} - 3 x ^{3} - 7 x ^{2} \times 7 x ^{2}}{x ^{2}}

Multiply

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Multiply the terms

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

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

- 49 x^{2 + 2}

Add the numbers

- 49 x^{4}

\frac{x ^{4} - 3 x ^{3} - 49 x ^{4}}{x ^{2}}

Subtract the terms

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Evaluate

x^{4} - 3 x^{3} - 49 x^{4}

Subtract the terms

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Evaluate

x^{4} - 49 x^{4}

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

(1 - 49) x^{4}

Subtract the numbers

- 48 x^{4}

- 48 x^{4} - 3 x^{3}

\frac{- 48 x ^{4} - 3 x ^{3}}{x ^{2}}

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

- \frac{48 x ^{4} + 3 x ^{3}}{x ^{2}}

Factor

- \frac{x ^{2} ( 48 x ^{2} + 3 x )}{x ^{2}}

Reduce the fraction

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

Solution

- 48 x^{2} - 3 x

Show Solution

Find the excluded values

x = 0

Evaluate

\frac{x ^{4} - 3 x ^{3} - 7 x ^{2} \times 7 x ^{2}}{x ^{2}}

To find the excluded values,set the denominators equal to 0

x^{2} = 0

Solution

x = 0

Show Solution

Find the roots

x = - \frac{1}{16}

Alternative Form

x = - 0.0625

Evaluate

\frac{x ^{4} - 3 x ^{3} - 7 x ^{2} \times 7 x ^{2}}{x ^{2}}

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

\frac{x ^{4} - 3 x ^{3} - 7 x ^{2} \times 7 x ^{2}}{x ^{2}} = 0

The only way a power can not be 0 is when the base not equals 0

\frac{x ^{4} - 3 x ^{3} - 7 x ^{2} \times 7 x ^{2}}{x ^{2}} = 0, x \neq = 0

Calculate

\frac{x ^{4} - 3 x ^{3} - 7 x ^{2} \times 7 x ^{2}}{x ^{2}} = 0

Multiply

More Steps

Multiply the terms

7 x^{2} \times 7 x^{2}

Multiply the terms

49 x^{2} \times x^{2}

Multiply the terms with the same base by adding their exponents

49 x^{2 + 2}

Add the numbers

49 x^{4}

\frac{x ^{4} - 3 x ^{3} - 49 x ^{4}}{x ^{2}} = 0

Subtract the terms

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Simplify

x^{4} - 3 x^{3} - 49 x^{4}

Subtract the terms

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Evaluate

x^{4} - 49 x^{4}

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

(1 - 49) x^{4}

Subtract the numbers

- 48 x^{4}

- 48 x^{4} - 3 x^{3}

\frac{- 48 x ^{4} - 3 x ^{3}}{x ^{2}} = 0

Divide the terms

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Evaluate

\frac{- 48 x ^{4} - 3 x ^{3}}{x ^{2}}

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

- \frac{48 x ^{4} + 3 x ^{3}}{x ^{2}}

Factor

- \frac{x ^{2} ( 48 x ^{2} + 3 x )}{x ^{2}}

Reduce the fraction

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

Calculate

- 48 x^{2} - 3 x

- 48 x^{2} - 3 x = 0

Factor the expression

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Evaluate

- 48 x^{2} - 3 x

Rewrite the expression

- 3 x \times 16 x - 3 x

Factor out - 3 x from the expression

- 3 x (16 x + 1)

- 3 x (16 x + 1) = 0

When the product of factors equals 0,at least one factor is 0

- 3 x = 0 16 x + 1 = 0

Solve the equation for x

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Evaluate

- 3 x = 0

Change the signs on both sides of the equation

3 x = 0

Rewrite the expression

x = 0

x = 0 16 x + 1 = 0

Solve the equation for x

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Evaluate

16 x + 1 = 0

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

16 x = 0 - 1

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

16 x = - 1

Divide both sides

\frac{16 x}{16} = \frac{- 1}{16}

Divide the numbers

x = \frac{- 1}{16}

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

x = - \frac{1}{16}

x = 0 x = - \frac{1}{16}

Check if the solution is in the defined range

x = 0 x = - \frac{1}{16}, x \neq = 0

Solution

x = - \frac{1}{16}

Alternative Form

x = - 0.0625

Show Solution