Solve 2x^4 9x^2-5

Question

Simplify the expression

18 x^{6} - 5

Evaluate

2 x^{4} \times 9 x^{2} - 5

Solution

More Steps

Evaluate

2 x^{4} \times 9 x^{2}

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

18 x^{4 + 2}

Add the numbers

18 x^{6}

18 x^{6} - 5

Show Solution

x_{1} = - \frac{6 5 \times 1 8 ^{5}}{18}, x_{2} = \frac{6 5 \times 1 8 ^{5}}{18}

Alternative Form

x_{1} \approx - 0.807761, x_{2} \approx 0.807761

Evaluate

2 x^{4} \times 9 x^{2} - 5

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

2 x^{4} \times 9 x^{2} - 5 = 0

Multiply

More Steps

Multiply the terms

2 x^{4} \times 9 x^{2}

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

18 x^{4 + 2}

Add the numbers

18 x^{6}

18 x^{6} - 5 = 0

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

18 x^{6} = 0 + 5

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

18 x^{6} = 5

Divide both sides

\frac{18 x ^{6}}{18} = \frac{5}{18}

Divide the numbers

x^{6} = \frac{5}{18}

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

x = \pm 6 \frac{5}{18}

Simplify the expression

More Steps

Evaluate

6 \frac{5}{18}

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

\frac{6 5}{6 18}

Multiply by the Conjugate

\frac{6 5 \times 6 1 8 ^{5}}{6 18 \times 6 1 8 ^{5}}

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

\frac{6 5 \times 1 8 ^{5}}{6 18 \times 6 1 8 ^{5}}

Multiply the numbers

More Steps

Evaluate

618 \times 6 1 8^{5}

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

6 18 \times 1 8^{5}

Calculate the product

6 1 8^{6}

Reduce the index of the radical and exponent with 6

18

\frac{6 5 \times 1 8 ^{5}}{18}

x = \pm \frac{6 5 \times 1 8 ^{5}}{18}

Separate the equation into 2 possible cases

x = \frac{6 5 \times 1 8 ^{5}}{18} x = - \frac{6 5 \times 1 8 ^{5}}{18}

Solution

x_{1} = - \frac{6 5 \times 1 8 ^{5}}{18}, x_{2} = \frac{6 5 \times 1 8 ^{5}}{18}

Alternative Form

x_{1} \approx - 0.807761, x_{2} \approx 0.807761

Show Solution