Solve 8x^6-204 - ScanMath

Question

Factor the expression

4 (2 x^{6} - 51)

Evaluate

8 x^{6} - 204

Solution

4 (2 x^{6} - 51)

Show Solution

x_{1} = - \frac{6 1632}{2}, x_{2} = \frac{6 1632}{2}

Alternative Form

x_{1} \approx - 1.715629, x_{2} \approx 1.715629

Evaluate

8 x^{6} - 204

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

8 x^{6} - 204 = 0

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

8 x^{6} = 0 + 204

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

8 x^{6} = 204

Divide both sides

\frac{8 x ^{6}}{8} = \frac{204}{8}

Divide the numbers

x^{6} = \frac{204}{8}

Cancel out the common factor 4

x^{6} = \frac{51}{2}

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

x = \pm 6 \frac{51}{2}

Simplify the expression

More Steps

Evaluate

6 \frac{51}{2}

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

\frac{6 51}{6 2}

Multiply by the Conjugate

\frac{6 51 \times 6 2 ^{5}}{6 2 \times 6 2 ^{5}}

Simplify

\frac{6 51 \times 6 32}{6 2 \times 6 2 ^{5}}

Multiply the numbers

More Steps

Evaluate

651 \times 632

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

6 51 \times 32

Calculate the product

61632

\frac{6 1632}{6 2 \times 6 2 ^{5}}

Multiply the numbers

More Steps

Evaluate

62 \times 6 2^{5}

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

6 2 \times 2^{5}

Calculate the product

6 2^{6}

Reduce the index of the radical and exponent with 6

2

\frac{6 1632}{2}

x = \pm \frac{6 1632}{2}

Separate the equation into 2 possible cases

x = \frac{6 1632}{2} x = - \frac{6 1632}{2}

Solution

x_{1} = - \frac{6 1632}{2}, x_{2} = \frac{6 1632}{2}

Alternative Form

x_{1} \approx - 1.715629, x_{2} \approx 1.715629

Show Solution