Solve b^630-10-306

Question

Simplify the expression

30 b^{6} - 316

Evaluate

b^{6} \times 30 - 10 - 306

Use the commutative property to reorder the terms

30 b^{6} - 10 - 306

Solution

30 b^{6} - 316

Show Solution

2 (15 b^{6} - 158)

Evaluate

b^{6} \times 30 - 10 - 306

Use the commutative property to reorder the terms

30 b^{6} - 10 - 306

Subtract the numbers

30 b^{6} - 316

Solution

2 (15 b^{6} - 158)

Show Solution

b_{1} = - \frac{6 158 \times 1 5 ^{5}}{15}, b_{2} = \frac{6 158 \times 1 5 ^{5}}{15}

Alternative Form

b_{1} \approx - 1.480566, b_{2} \approx 1.480566

Evaluate

b^{6} \times 30 - 10 - 306

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

b^{6} \times 30 - 10 - 306 = 0

Use the commutative property to reorder the terms

30 b^{6} - 10 - 306 = 0

Subtract the numbers

30 b^{6} - 316 = 0

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

30 b^{6} = 0 + 316

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

30 b^{6} = 316

Divide both sides

\frac{30 b ^{6}}{30} = \frac{316}{30}

Divide the numbers

b^{6} = \frac{316}{30}

Cancel out the common factor 2

b^{6} = \frac{158}{15}

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

b = \pm 6 \frac{158}{15}

Simplify the expression

More Steps

Evaluate

6 \frac{158}{15}

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

\frac{6 158}{6 15}

Multiply by the Conjugate

\frac{6 158 \times 6 1 5 ^{5}}{6 15 \times 6 1 5 ^{5}}

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

\frac{6 158 \times 1 5 ^{5}}{6 15 \times 6 1 5 ^{5}}

Multiply the numbers

More Steps

Evaluate

615 \times 6 1 5^{5}

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

6 15 \times 1 5^{5}

Calculate the product

6 1 5^{6}

Reduce the index of the radical and exponent with 6

15

\frac{6 158 \times 1 5 ^{5}}{15}

b = \pm \frac{6 158 \times 1 5 ^{5}}{15}

Separate the equation into 2 possible cases

b = \frac{6 158 \times 1 5 ^{5}}{15} b = - \frac{6 158 \times 1 5 ^{5}}{15}

Solution

b_{1} = - \frac{6 158 \times 1 5 ^{5}}{15}, b_{2} = \frac{6 158 \times 1 5 ^{5}}{15}

Alternative Form

b_{1} \approx - 1.480566, b_{2} \approx 1.480566

Show Solution