Solve x^(4) 4x^(2)-45

Question

Simplify the expression

4 x^{6} - 45

Evaluate

x^{4} \times 4 x^{2} - 45

Solution

More Steps

Evaluate

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

Multiply the terms with the same base by adding their exponents

x^{4 + 2} \times 4

Add the numbers

x^{6} \times 4

Use the commutative property to reorder the terms

4 x^{6}

4 x^{6} - 45

Show Solution

x_{1} = - \frac{6 720}{2}, x_{2} = \frac{6 720}{2}

Alternative Form

x_{1} \approx - 1.496898, x_{2} \approx 1.496898

Evaluate

x^{4} \times 4 x^{2} - 45

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

x^{4} \times 4 x^{2} - 45 = 0

Multiply

More Steps

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

x^{4 + 2} \times 4

Add the numbers

x^{6} \times 4

Use the commutative property to reorder the terms

4 x^{6}

4 x^{6} - 45 = 0

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

4 x^{6} = 0 + 45

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

4 x^{6} = 45

Divide both sides

\frac{4 x ^{6}}{4} = \frac{45}{4}

Divide the numbers

x^{6} = \frac{45}{4}

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

x = \pm 6 \frac{45}{4}

Simplify the expression

More Steps

Evaluate

6 \frac{45}{4}

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

\frac{6 45}{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 45}{3 2}

Multiply by the Conjugate

\frac{6 45 \times 3 2 ^{2}}{3 2 \times 3 2 ^{2}}

Simplify

\frac{6 45 \times 3 4}{3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

645 \times 34

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

645 \times 6 4^{2}

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

6 45 \times 4^{2}

Calculate the product

6720

\frac{6 720}{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{6 720}{2}

x = \pm \frac{6 720}{2}

Separate the equation into 2 possible cases

x = \frac{6 720}{2} x = - \frac{6 720}{2}

Solution

x_{1} = - \frac{6 720}{2}, x_{2} = \frac{6 720}{2}

Alternative Form

x_{1} \approx - 1.496898, x_{2} \approx 1.496898

Show Solution