Solve x^(4) 15x^(2)-16

Question

Simplify the expression

15 x^{6} - 16

Evaluate

x^{4} \times 15 x^{2} - 16

Solution

More Steps

Evaluate

x^{4} \times 15 x^{2}

Multiply the terms with the same base by adding their exponents

x^{4 + 2} \times 15

Add the numbers

x^{6} \times 15

Use the commutative property to reorder the terms

15 x^{6}

15 x^{6} - 16

Show Solution

x_{1} = - \frac{6 16 \times 1 5 ^{5}}{15}, x_{2} = \frac{6 16 \times 1 5 ^{5}}{15}

Alternative Form

x_{1} \approx - 1.010814, x_{2} \approx 1.010814

Evaluate

x^{4} \times 15 x^{2} - 16

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

x^{4} \times 15 x^{2} - 16 = 0

Multiply

More Steps

Multiply the terms

x^{4} \times 15 x^{2}

Multiply the terms with the same base by adding their exponents

x^{4 + 2} \times 15

Add the numbers

x^{6} \times 15

Use the commutative property to reorder the terms

15 x^{6}

15 x^{6} - 16 = 0

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

15 x^{6} = 0 + 16

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

15 x^{6} = 16

Divide both sides

\frac{15 x ^{6}}{15} = \frac{16}{15}

Divide the numbers

x^{6} = \frac{16}{15}

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

x = \pm 6 \frac{16}{15}

Simplify the expression

More Steps

Evaluate

6 \frac{16}{15}

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

\frac{6 16}{6 15}

Simplify the radical expression

\frac{3 4}{6 15}

Multiply by the Conjugate

\frac{3 4 \times 6 1 5 ^{5}}{6 15 \times 6 1 5 ^{5}}

Multiply the numbers

More Steps

Evaluate

34 \times 6 1 5^{5}

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

6 4^{2} \times 6 1 5^{5}

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

6 4^{2} \times 1 5^{5}

Calculate the product

6 16 \times 1 5^{5}

\frac{6 16 \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 16 \times 1 5 ^{5}}{15}

x = \pm \frac{6 16 \times 1 5 ^{5}}{15}

Separate the equation into 2 possible cases

x = \frac{6 16 \times 1 5 ^{5}}{15} x = - \frac{6 16 \times 1 5 ^{5}}{15}

Solution

x_{1} = - \frac{6 16 \times 1 5 ^{5}}{15}, x_{2} = \frac{6 16 \times 1 5 ^{5}}{15}

Alternative Form

x_{1} \approx - 1.010814, x_{2} \approx 1.010814

Show Solution