Solve x^2 4x^4 = 18

Question

Solve the equation

x_{1} = - \frac{6 288}{2}, x_{2} = \frac{6 288}{2}

Alternative Form

x_{1} \approx - 1.284898, x_{2} \approx 1.284898

Evaluate

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

Multiply

More Steps

Evaluate

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

Multiply the terms with the same base by adding their exponents

x^{2 + 4} \times 4

Add the numbers

x^{6} \times 4

Use the commutative property to reorder the terms

4 x^{6}

4 x^{6} = 18

Divide both sides

\frac{4 x ^{6}}{4} = \frac{18}{4}

Divide the numbers

x^{6} = \frac{18}{4}

Cancel out the common factor 2

x^{6} = \frac{9}{2}

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

x = \pm 6 \frac{9}{2}

Simplify the expression

More Steps

Evaluate

6 \frac{9}{2}

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

\frac{6 9}{6 2}

Simplify the radical expression

More Steps

Evaluate

69

Write the number in exponential form with the base of 3

6 3^{2}

Reduce the index of the radical and exponent with 2

33

\frac{3 3}{6 2}

Multiply by the Conjugate

\frac{3 3 \times 6 2 ^{5}}{6 2 \times 6 2 ^{5}}

Simplify

\frac{3 3 \times 6 32}{6 2 \times 6 2 ^{5}}

Multiply the numbers

More Steps

Evaluate

33 \times 632

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

6 3^{2} \times 632

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

6 3^{2} \times 32

Calculate the product

6288

\frac{6 288}{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{6 288}{2}

x = \pm \frac{6 288}{2}

Separate the equation into 2 possible cases

x = \frac{6 288}{2} x = - \frac{6 288}{2}

Solution

x_{1} = - \frac{6 288}{2}, x_{2} = \frac{6 288}{2}

Alternative Form

x_{1} \approx - 1.284898, x_{2} \approx 1.284898

Show Solution