Solve 5b^(2) 15b-19=0

Question

Solve the equation

b = \frac{3 855}{15}

Alternative Form

b \approx 0.632748

Evaluate

5 b^{2} \times 15 b - 19 = 0

Multiply

More Steps

Evaluate

5 b^{2} \times 15 b

Multiply the terms

75 b^{2} \times b

Multiply the terms with the same base by adding their exponents

75 b^{2 + 1}

Add the numbers

75 b^{3}

75 b^{3} - 19 = 0

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

75 b^{3} = 0 + 19

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

75 b^{3} = 19

Divide both sides

\frac{75 b ^{3}}{75} = \frac{19}{75}

Divide the numbers

b^{3} = \frac{19}{75}

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

3 b^{3} = 3 \frac{19}{75}

Calculate

b = 3 \frac{19}{75}

Solution

More Steps

Evaluate

3 \frac{19}{75}

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

\frac{3 19}{3 75}

Multiply by the Conjugate

\frac{3 19 \times 3 7 5 ^{2}}{3 75 \times 3 7 5 ^{2}}

Simplify

\frac{3 19 \times 5 3 45}{3 75 \times 3 7 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

319 \times 5345

Multiply the terms

3855 \times 5

Use the commutative property to reorder the terms

53855

\frac{5 3 855}{3 75 \times 3 7 5 ^{2}}

Multiply the numbers

More Steps

Evaluate

375 \times 3 7 5^{2}

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

3 75 \times 7 5^{2}

Calculate the product

3 7 5^{3}

Reduce the index of the radical and exponent with 3

75

\frac{5 3 855}{75}

Cancel out the common factor 5

\frac{3 855}{15}

b = \frac{3 855}{15}

Alternative Form

b \approx 0.632748

Show Solution