Solve b^630-10-602

Question

Simplify the expression

30 b^{6} - 612

Evaluate

b^{6} \times 30 - 10 - 602

Use the commutative property to reorder the terms

30 b^{6} - 10 - 602

Solution

30 b^{6} - 612

Show Solution

6 (5 b^{6} - 102)

Evaluate

b^{6} \times 30 - 10 - 602

Use the commutative property to reorder the terms

30 b^{6} - 10 - 602

Subtract the numbers

30 b^{6} - 612

Solution

6 (5 b^{6} - 102)

Show Solution

b_{1} = - \frac{6 318750}{5}, b_{2} = \frac{6 318750}{5}

Alternative Form

b_{1} \approx - 1.652996, b_{2} \approx 1.652996

Evaluate

b^{6} \times 30 - 10 - 602

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

b^{6} \times 30 - 10 - 602 = 0

Use the commutative property to reorder the terms

30 b^{6} - 10 - 602 = 0

Subtract the numbers

30 b^{6} - 612 = 0

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

30 b^{6} = 0 + 612

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

30 b^{6} = 612

Divide both sides

\frac{30 b ^{6}}{30} = \frac{612}{30}

Divide the numbers

b^{6} = \frac{612}{30}

Cancel out the common factor 6

b^{6} = \frac{102}{5}

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

b = \pm 6 \frac{102}{5}

Simplify the expression

More Steps

Evaluate

6 \frac{102}{5}

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

\frac{6 102}{6 5}

Multiply by the Conjugate

\frac{6 102 \times 6 5 ^{5}}{6 5 \times 6 5 ^{5}}

Simplify

\frac{6 102 \times 6 3125}{6 5 \times 6 5 ^{5}}

Multiply the numbers

More Steps

Evaluate

6102 \times 63125

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

6 102 \times 3125

Calculate the product

6318750

\frac{6 318750}{6 5 \times 6 5 ^{5}}

Multiply the numbers

More Steps

Evaluate

65 \times 6 5^{5}

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

6 5 \times 5^{5}

Calculate the product

6 5^{6}

Reduce the index of the radical and exponent with 6

5

\frac{6 318750}{5}

b = \pm \frac{6 318750}{5}

Separate the equation into 2 possible cases

b = \frac{6 318750}{5} b = - \frac{6 318750}{5}

Solution

b_{1} = - \frac{6 318750}{5}, b_{2} = \frac{6 318750}{5}

Alternative Form

b_{1} \approx - 1.652996, b_{2} \approx 1.652996

Show Solution