Solve 4b^217b 15=b

Question

Solve the equation

b_{1} = - \frac{255}{510}, b_{2} = 0, b_{3} = \frac{255}{510}

Alternative Form

b_{1} \approx - 0.031311, b_{2} = 0, b_{3} \approx 0.031311

Evaluate

4 b^{2} \times 17 b \times 15 = b

Multiply

More Steps

Evaluate

4 b^{2} \times 17 b \times 15

Multiply the terms

More Steps

Evaluate

4 \times 17 \times 15

Multiply the terms

68 \times 15

Multiply the numbers

1020

1020 b^{2} \times b

Multiply the terms with the same base by adding their exponents

1020 b^{2 + 1}

Add the numbers

1020 b^{3}

1020 b^{3} = b

Add or subtract both sides

1020 b^{3} - b = 0

Factor the expression

b (1020 b^{2} - 1) = 0

Separate the equation into 2 possible cases

b = 0 1020 b^{2} - 1 = 0

Solve the equation

More Steps

Evaluate

1020 b^{2} - 1 = 0

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

1020 b^{2} = 0 + 1

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

1020 b^{2} = 1

Divide both sides

\frac{1020 b ^{2}}{1020} = \frac{1}{1020}

Divide the numbers

b^{2} = \frac{1}{1020}

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

b = \pm \frac{1}{1020}

Simplify the expression

More Steps

Evaluate

\frac{1}{1020}

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

\frac{1}{1020}

Simplify the radical expression

\frac{1}{1020}

Simplify the radical expression

\frac{1}{2 255}

Multiply by the Conjugate

\frac{255}{2 255 \times 255}

Multiply the numbers

\frac{255}{510}

b = \pm \frac{255}{510}

Separate the equation into 2 possible cases

b = \frac{255}{510} b = - \frac{255}{510}

b = 0 b = \frac{255}{510} b = - \frac{255}{510}

Solution

b_{1} = - \frac{255}{510}, b_{2} = 0, b_{3} = \frac{255}{510}

Alternative Form

b_{1} \approx - 0.031311, b_{2} = 0, b_{3} \approx 0.031311

Show Solution