Solve 2l^3-1/2*3-1/2*7/16

Question

Simplify the expression

2 l^{3} - \frac{55}{32}

Evaluate

2 l^{3} - \frac{1}{2} \times 3 - \frac{1}{2} \times \frac{7}{16}

Multiply the numbers

2 l^{3} - \frac{3}{2} - \frac{1}{2} \times \frac{7}{16}

Multiply the numbers

More Steps

Evaluate

- \frac{1}{2} \times \frac{7}{16}

To multiply the fractions,multiply the numerators and denominators separately

- \frac{7}{2 \times 16}

Multiply the numbers

- \frac{7}{32}

2 l^{3} - \frac{3}{2} - \frac{7}{32}

Solution

More Steps

Evaluate

- \frac{3}{2} - \frac{7}{32}

Reduce fractions to a common denominator

- \frac{3 \times 16}{2 \times 16} - \frac{7}{32}

Multiply the numbers

- \frac{3 \times 16}{32} - \frac{7}{32}

Write all numerators above the common denominator

\frac{- 3 \times 16 - 7}{32}

Multiply the numbers

\frac{- 48 - 7}{32}

Subtract the numbers

\frac{- 55}{32}

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

- \frac{55}{32}

2 l^{3} - \frac{55}{32}

Show Solution

Factor the expression

\frac{1}{32} (64 l^{3} - 55)

Evaluate

2 l^{3} - \frac{1}{2} \times 3 - \frac{1}{2} \times \frac{7}{16}

Multiply the numbers

2 l^{3} - \frac{3}{2} - \frac{1}{2} \times \frac{7}{16}

Multiply the numbers

More Steps

Evaluate

\frac{1}{2} \times \frac{7}{16}

To multiply the fractions,multiply the numerators and denominators separately

\frac{7}{2 \times 16}

Multiply the numbers

\frac{7}{32}

2 l^{3} - \frac{3}{2} - \frac{7}{32}

Subtract the numbers

More Steps

Evaluate

- \frac{3}{2} - \frac{7}{32}

Reduce fractions to a common denominator

- \frac{3 \times 16}{2 \times 16} - \frac{7}{32}

Multiply the numbers

- \frac{3 \times 16}{32} - \frac{7}{32}

Write all numerators above the common denominator

\frac{- 3 \times 16 - 7}{32}

Multiply the numbers

\frac{- 48 - 7}{32}

Subtract the numbers

\frac{- 55}{32}

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

- \frac{55}{32}

2 l^{3} - \frac{55}{32}

Solution

\frac{1}{32} (64 l^{3} - 55)

Show Solution

Find the roots

l = \frac{3 55}{4}

Alternative Form

l \approx 0.950738

Evaluate

2 l^{3} - \frac{1}{2} \times 3 - \frac{1}{2} \times \frac{7}{16}

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

2 l^{3} - \frac{1}{2} \times 3 - \frac{1}{2} \times \frac{7}{16} = 0

Multiply the numbers

2 l^{3} - \frac{3}{2} - \frac{1}{2} \times \frac{7}{16} = 0

Multiply the numbers

More Steps

Evaluate

\frac{1}{2} \times \frac{7}{16}

To multiply the fractions,multiply the numerators and denominators separately

\frac{7}{2 \times 16}

Multiply the numbers

\frac{7}{32}

2 l^{3} - \frac{3}{2} - \frac{7}{32} = 0

Subtract the numbers

More Steps

Simplify

2 l^{3} - \frac{3}{2} - \frac{7}{32}

Subtract the numbers

More Steps

Evaluate

- \frac{3}{2} - \frac{7}{32}

Reduce fractions to a common denominator

- \frac{3 \times 16}{2 \times 16} - \frac{7}{32}

Multiply the numbers

- \frac{3 \times 16}{32} - \frac{7}{32}

Write all numerators above the common denominator

\frac{- 3 \times 16 - 7}{32}

Multiply the numbers

\frac{- 48 - 7}{32}

Subtract the numbers

\frac{- 55}{32}

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

- \frac{55}{32}

2 l^{3} - \frac{55}{32}

2 l^{3} - \frac{55}{32} = 0

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

2 l^{3} = 0 + \frac{55}{32}

Add the terms

2 l^{3} = \frac{55}{32}

Multiply by the reciprocal

2 l^{3} \times \frac{1}{2} = \frac{55}{32} \times \frac{1}{2}

Multiply

l^{3} = \frac{55}{32} \times \frac{1}{2}

Multiply

More Steps

Evaluate

\frac{55}{32} \times \frac{1}{2}

To multiply the fractions,multiply the numerators and denominators separately

\frac{55}{32 \times 2}

Multiply the numbers

\frac{55}{64}

l^{3} = \frac{55}{64}

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

3 l^{3} = 3 \frac{55}{64}

Calculate

l = 3 \frac{55}{64}

Solution

More Steps

Evaluate

3 \frac{55}{64}

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

\frac{3 55}{3 64}

Simplify the radical expression

More Steps

Evaluate

364

Write the number in exponential form with the base of 4

3 4^{3}

Reduce the index of the radical and exponent with 3

4

\frac{3 55}{4}

l = \frac{3 55}{4}

Alternative Form

l \approx 0.950738

Show Solution