Solve b^(2) 2b-483=0

Question

Solve the equation

b = \frac{3 1932}{2}

Alternative Form

b \approx 6.227385

Evaluate

b^{2} \times 2 b - 483 = 0

Multiply

More Steps

Evaluate

b^{2} \times 2 b

Multiply the terms with the same base by adding their exponents

b^{2 + 1} \times 2

Add the numbers

b^{3} \times 2

Use the commutative property to reorder the terms

2 b^{3}

2 b^{3} - 483 = 0

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

2 b^{3} = 0 + 483

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

2 b^{3} = 483

Divide both sides

\frac{2 b ^{3}}{2} = \frac{483}{2}

Divide the numbers

b^{3} = \frac{483}{2}

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

3 b^{3} = 3 \frac{483}{2}

Calculate

b = 3 \frac{483}{2}

Solution

More Steps

Evaluate

3 \frac{483}{2}

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

\frac{3 483}{3 2}

Multiply by the Conjugate

\frac{3 483 \times 3 2 ^{2}}{3 2 \times 3 2 ^{2}}

Simplify

\frac{3 483 \times 3 4}{3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

3483 \times 34

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

3 483 \times 4

Calculate the product

31932

\frac{3 1932}{3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

32 \times 3 2^{2}

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

3 2 \times 2^{2}

Calculate the product

3 2^{3}

Reduce the index of the radical and exponent with 3

2

\frac{3 1932}{2}

b = \frac{3 1932}{2}

Alternative Form

b \approx 6.227385

Show Solution