Solve 8x^2 4x-(7/2)

Question

Simplify the expression

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

Evaluate

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

Solution

More Steps

Evaluate

8 x^{2} \times 4 x

Multiply the terms

32 x^{2} \times x

Multiply the terms with the same base by adding their exponents

32 x^{2 + 1}

Add the numbers

32 x^{3}

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

Show Solution

Factor the expression

\frac{1}{2} (64 x^{3} - 7)

Evaluate

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

Multiply

More Steps

Evaluate

8 x^{2} \times 4 x

Multiply the terms

32 x^{2} \times x

Multiply the terms with the same base by adding their exponents

32 x^{2 + 1}

Add the numbers

32 x^{3}

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

Solution

\frac{1}{2} (64 x^{3} - 7)

Show Solution

Find the roots

x = \frac{3 7}{4}

Alternative Form

x \approx 0.478233

Evaluate

8 x^{2} \times 4 x - (\frac{7}{2})

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

8 x^{2} \times 4 x - (\frac{7}{2}) = 0

Remove the unnecessary parentheses

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

Multiply

More Steps

Multiply the terms

8 x^{2} \times 4 x

Multiply the terms

32 x^{2} \times x

Multiply the terms with the same base by adding their exponents

32 x^{2 + 1}

Add the numbers

32 x^{3}

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

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

32 x^{3} = 0 + \frac{7}{2}

Add the terms

32 x^{3} = \frac{7}{2}

Multiply by the reciprocal

32 x^{3} \times \frac{1}{32} = \frac{7}{2} \times \frac{1}{32}

Multiply

x^{3} = \frac{7}{2} \times \frac{1}{32}

Multiply

More Steps

Evaluate

\frac{7}{2} \times \frac{1}{32}

To multiply the fractions,multiply the numerators and denominators separately

\frac{7}{2 \times 32}

Multiply the numbers

\frac{7}{64}

x^{3} = \frac{7}{64}

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

3 x^{3} = 3 \frac{7}{64}

Calculate

x = 3 \frac{7}{64}

Solution

More Steps

Evaluate

3 \frac{7}{64}

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

\frac{3 7}{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 7}{4}

x = \frac{3 7}{4}

Alternative Form

x \approx 0.478233

Show Solution