Solve 8x^6-214 - ScanMath

Question

Factor the expression

2 (4 x^{6} - 107)

Evaluate

8 x^{6} - 214

Solution

2 (4 x^{6} - 107)

Show Solution

x_{1} = - \frac{6 1712}{2}, x_{2} = \frac{6 1712}{2}

Alternative Form

x_{1} \approx - 1.729368, x_{2} \approx 1.729368

Evaluate

8 x^{6} - 214

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

8 x^{6} - 214 = 0

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

8 x^{6} = 0 + 214

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

8 x^{6} = 214

Divide both sides

\frac{8 x ^{6}}{8} = \frac{214}{8}

Divide the numbers

x^{6} = \frac{214}{8}

Cancel out the common factor 2

x^{6} = \frac{107}{4}

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

x = \pm 6 \frac{107}{4}

Simplify the expression

More Steps

Evaluate

6 \frac{107}{4}

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

\frac{6 107}{6 4}

Simplify the radical expression

More Steps

Evaluate

64

Write the number in exponential form with the base of 2

6 2^{2}

Reduce the index of the radical and exponent with 2

32

\frac{6 107}{3 2}

Multiply by the Conjugate

\frac{6 107 \times 3 2 ^{2}}{3 2 \times 3 2 ^{2}}

Simplify

\frac{6 107 \times 3 4}{3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

6107 \times 34

Use n a = mn a^{m} to expand the expression

6107 \times 6 4^{2}

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

6 107 \times 4^{2}

Calculate the product

61712

\frac{6 1712}{3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

32 \times 3 2^{2}

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

3 2 \times 2^{2}

Calculate the product

3 2^{3}

Reduce the index of the radical and exponent with 3

2

\frac{6 1712}{2}

x = \pm \frac{6 1712}{2}

Separate the equation into 2 possible cases

x = \frac{6 1712}{2} x = - \frac{6 1712}{2}

Solution

x_{1} = - \frac{6 1712}{2}, x_{2} = \frac{6 1712}{2}

Alternative Form

x_{1} \approx - 1.729368, x_{2} \approx 1.729368

Show Solution