Solve x^2 1/16x^2 1/2 - 7x - 7/4x

Question

Simplify the expression

\frac{1}{32} x^{4} - \frac{35}{4} x

Evaluate

x^{2} \times \frac{1}{16} x^{2} \times \frac{1}{2} - 7 x - \frac{7}{4} x

Multiply

More Steps

Multiply the terms

x^{2} \times \frac{1}{16} x^{2} \times \frac{1}{2}

Multiply the terms with the same base by adding their exponents

x^{2 + 2} \times \frac{1}{16} \times \frac{1}{2}

Add the numbers

x^{4} \times \frac{1}{16} \times \frac{1}{2}

Multiply the terms

More Steps

Evaluate

\frac{1}{16} \times \frac{1}{2}

To multiply the fractions,multiply the numerators and denominators separately

\frac{1}{16 \times 2}

Multiply the numbers

\frac{1}{32}

x^{4} \times \frac{1}{32}

Use the commutative property to reorder the terms

\frac{1}{32} x^{4}

\frac{1}{32} x^{4} - 7 x - \frac{7}{4} x

Solution

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Evaluate

- 7 x - \frac{7}{4} x

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

(- 7 - \frac{7}{4}) x

Subtract the numbers

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Evaluate

- 7 - \frac{7}{4}

Reduce fractions to a common denominator

- \frac{7 \times 4}{4} - \frac{7}{4}

Write all numerators above the common denominator

\frac{- 7 \times 4 - 7}{4}

Multiply the numbers

\frac{- 28 - 7}{4}

Subtract the numbers

\frac{- 35}{4}

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

- \frac{35}{4}

- \frac{35}{4} x

\frac{1}{32} x^{4} - \frac{35}{4} x

Show Solution

Factor the expression

\frac{1}{32} x (x^{3} - 280)

Evaluate

x^{2} \times \frac{1}{16} x^{2} \times \frac{1}{2} - 7 x - \frac{7}{4} x

Multiply

More Steps

Multiply the terms

x^{2} \times \frac{1}{16} x^{2} \times \frac{1}{2}

Multiply the terms with the same base by adding their exponents

x^{2 + 2} \times \frac{1}{16} \times \frac{1}{2}

Add the numbers

x^{4} \times \frac{1}{16} \times \frac{1}{2}

Multiply the terms

More Steps

Evaluate

\frac{1}{16} \times \frac{1}{2}

To multiply the fractions,multiply the numerators and denominators separately

\frac{1}{16 \times 2}

Multiply the numbers

\frac{1}{32}

x^{4} \times \frac{1}{32}

Use the commutative property to reorder the terms

\frac{1}{32} x^{4}

\frac{1}{32} x^{4} - 7 x - \frac{7}{4} x

Subtract the terms

More Steps

Evaluate

- 7 x - \frac{7}{4} x

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

(- 7 - \frac{7}{4}) x

Subtract the numbers

More Steps

Evaluate

- 7 - \frac{7}{4}

Reduce fractions to a common denominator

- \frac{7 \times 4}{4} - \frac{7}{4}

Write all numerators above the common denominator

\frac{- 7 \times 4 - 7}{4}

Multiply the numbers

\frac{- 28 - 7}{4}

Subtract the numbers

\frac{- 35}{4}

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

- \frac{35}{4}

- \frac{35}{4} x

\frac{1}{32} x^{4} - \frac{35}{4} x

Rewrite the expression

\frac{1}{32} x \times x^{3} - \frac{1}{32} x \times 280

Solution

\frac{1}{32} x (x^{3} - 280)

Show Solution

Find the roots

x_{1} = 0, x_{2} = 2335

Alternative Form

x_{1} = 0, x_{2} \approx 6.542133

Evaluate

x^{2} \times \frac{1}{16} x^{2} \times \frac{1}{2} - 7 x - \frac{7}{4} x

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

x^{2} \times \frac{1}{16} x^{2} \times \frac{1}{2} - 7 x - \frac{7}{4} x = 0

Multiply

More Steps

Multiply the terms

x^{2} \times \frac{1}{16} x^{2} \times \frac{1}{2}

Multiply the terms with the same base by adding their exponents

x^{2 + 2} \times \frac{1}{16} \times \frac{1}{2}

Add the numbers

x^{4} \times \frac{1}{16} \times \frac{1}{2}

Multiply the terms

More Steps

Evaluate

\frac{1}{16} \times \frac{1}{2}

To multiply the fractions,multiply the numerators and denominators separately

\frac{1}{16 \times 2}

Multiply the numbers

\frac{1}{32}

x^{4} \times \frac{1}{32}

Use the commutative property to reorder the terms

\frac{1}{32} x^{4}

\frac{1}{32} x^{4} - 7 x - \frac{7}{4} x = 0

Subtract the terms

More Steps

Simplify

\frac{1}{32} x^{4} - 7 x - \frac{7}{4} x

Subtract the terms

More Steps

Evaluate

- 7 x - \frac{7}{4} x

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

(- 7 - \frac{7}{4}) x

Subtract the numbers

- \frac{35}{4} x

\frac{1}{32} x^{4} - \frac{35}{4} x

\frac{1}{32} x^{4} - \frac{35}{4} x = 0

Factor the expression

x (\frac{1}{32} x^{3} - \frac{35}{4}) = 0

Separate the equation into 2 possible cases

x = 0 \frac{1}{32} x^{3} - \frac{35}{4} = 0

Solve the equation

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Evaluate

\frac{1}{32} x^{3} - \frac{35}{4} = 0

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

\frac{1}{32} x^{3} = 0 + \frac{35}{4}

Add the terms

\frac{1}{32} x^{3} = \frac{35}{4}

Multiply by the reciprocal

\frac{1}{32} x^{3} \times 32 = \frac{35}{4} \times 32

Multiply

x^{3} = \frac{35}{4} \times 32

Multiply

More Steps

Evaluate

\frac{35}{4} \times 32

Reduce the numbers

35 \times 8

Multiply the numbers

280

x^{3} = 280

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

3 x^{3} = 3280

Calculate

x = 3280

Simplify the root

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Evaluate

3280

Write the expression as a product where the root of one of the factors can be evaluated

3 8 \times 35

Write the number in exponential form with the base of 2

3 2^{3} \times 35

The root of a product is equal to the product of the roots of each factor

3 2^{3} \times 335

Reduce the index of the radical and exponent with 3

2335

x = 2335

x = 0 x = 2335

Solution

x_{1} = 0, x_{2} = 2335

Alternative Form

x_{1} = 0, x_{2} \approx 6.542133

Show Solution