Solve 4x^3 8x^2 x-3

Question

Simplify the expression

32 x^{6} - 3

Evaluate

4 x^{3} \times 8 x^{2} \times x - 3

Solution

More Steps

Evaluate

4 x^{3} \times 8 x^{2} \times x

Multiply the terms

32 x^{3} \times x^{2} \times x

Multiply the terms with the same base by adding their exponents

32 x^{3 + 2 + 1}

Add the numbers

32 x^{6}

32 x^{6} - 3

Show Solution

Find the roots

x_{1} = - \frac{6 6}{2}, x_{2} = \frac{6 6}{2}

Alternative Form

x_{1} \approx - 0.674003, x_{2} \approx 0.674003

Evaluate

4 x^{3} \times 8 x^{2} \times x - 3

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

4 x^{3} \times 8 x^{2} \times x - 3 = 0

Multiply

More Steps

Multiply the terms

4 x^{3} \times 8 x^{2} \times x

Multiply the terms

32 x^{3} \times x^{2} \times x

Multiply the terms with the same base by adding their exponents

32 x^{3 + 2 + 1}

Add the numbers

32 x^{6}

32 x^{6} - 3 = 0

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

32 x^{6} = 0 + 3

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

32 x^{6} = 3

Divide both sides

\frac{32 x ^{6}}{32} = \frac{3}{32}

Divide the numbers

x^{6} = \frac{3}{32}

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm 6 \frac{3}{32}

Simplify the expression

More Steps

Evaluate

6 \frac{3}{32}

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

\frac{6 3}{6 32}

Multiply by the Conjugate

\frac{6 3 \times 6 3 2 ^{5}}{6 32 \times 6 3 2 ^{5}}

Simplify

\frac{6 3 \times 2 ^{4} 6 2}{6 32 \times 6 3 2 ^{5}}

Multiply the numbers

More Steps

Evaluate

63 \times 2^{4} 62

Multiply the terms

66 \times 2^{4}

Use the commutative property to reorder the terms

2^{4} 66

\frac{2 ^{4} 6 6}{6 32 \times 6 3 2 ^{5}}

Multiply the numbers

More Steps

Evaluate

632 \times 6 3 2^{5}

The product of roots with the same index is equal to the root of the product

6 32 \times 3 2^{5}

Calculate the product

6 3 2^{6}

Transform the expression

6 2^{30}

Reduce the index of the radical and exponent with 6

2^{5}

\frac{2 ^{4} 6 6}{2 ^{5}}

Reduce the fraction

More Steps

Evaluate

\frac{2 ^{4}}{2 ^{5}}

Use the product rule \frac{a ^{n}}{a ^{m}} = a^{n - m} to simplify the expression

\frac{1}{2 ^{5 - 4}}

Subtract the terms

\frac{1}{2 ^{1}}

Simplify

\frac{1}{2}

\frac{6 6}{2}

x = \pm \frac{6 6}{2}

Separate the equation into 2 possible cases

x = \frac{6 6}{2} x = - \frac{6 6}{2}

Solution

x_{1} = - \frac{6 6}{2}, x_{2} = \frac{6 6}{2}

Alternative Form

x_{1} \approx - 0.674003, x_{2} \approx 0.674003

Show Solution