Solve 15x^6-6 - ScanMath

Question

Factor the expression

3 (5 x^{6} - 2)

Evaluate

15 x^{6} - 6

Solution

3 (5 x^{6} - 2)

Show Solution

x_{1} = - \frac{6 6250}{5}, x_{2} = \frac{6 6250}{5}

Alternative Form

x_{1} \approx - 0.858374, x_{2} \approx 0.858374

Evaluate

15 x^{6} - 6

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

15 x^{6} - 6 = 0

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

15 x^{6} = 0 + 6

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

15 x^{6} = 6

Divide both sides

\frac{15 x ^{6}}{15} = \frac{6}{15}

Divide the numbers

x^{6} = \frac{6}{15}

Cancel out the common factor 3

x^{6} = \frac{2}{5}

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

x = \pm 6 \frac{2}{5}

Simplify the expression

More Steps

Evaluate

6 \frac{2}{5}

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

\frac{6 2}{6 5}

Multiply by the Conjugate

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

Simplify

\frac{6 2 \times 6 3125}{6 5 \times 6 5 ^{5}}

Multiply the numbers

More Steps

Evaluate

62 \times 63125

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

6 2 \times 3125

Calculate the product

66250

\frac{6 6250}{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 6250}{5}

x = \pm \frac{6 6250}{5}

Separate the equation into 2 possible cases

x = \frac{6 6250}{5} x = - \frac{6 6250}{5}

Solution

x_{1} = - \frac{6 6250}{5}, x_{2} = \frac{6 6250}{5}

Alternative Form

x_{1} \approx - 0.858374, x_{2} \approx 0.858374

Show Solution