Solve (x^2)4 (x^2)2 -12=0

Question

Solve the equation

x_{1} = - \frac{4 24}{2}, x_{2} = \frac{4 24}{2}

Alternative Form

x_{1} \approx - 1.106682, x_{2} \approx 1.106682

Evaluate

x^{2} \times 4 x^{2} \times 2 - 12 = 0

Multiply

More Steps

Evaluate

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

Multiply the terms with the same base by adding their exponents

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

Add the numbers

x^{4} \times 4 \times 2

Multiply the terms

x^{4} \times 8

Use the commutative property to reorder the terms

8 x^{4}

8 x^{4} - 12 = 0

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

8 x^{4} = 0 + 12

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

8 x^{4} = 12

Divide both sides

\frac{8 x ^{4}}{8} = \frac{12}{8}

Divide the numbers

x^{4} = \frac{12}{8}

Cancel out the common factor 4

x^{4} = \frac{3}{2}

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

x = \pm 4 \frac{3}{2}

Simplify the expression

More Steps

Evaluate

4 \frac{3}{2}

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

\frac{4 3}{4 2}

Multiply by the Conjugate

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

Simplify

\frac{4 3 \times 4 8}{4 2 \times 4 2 ^{3}}

Multiply the numbers

More Steps

Evaluate

43 \times 48

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

4 3 \times 8

Calculate the product

424

\frac{4 24}{4 2 \times 4 2 ^{3}}

Multiply the numbers

More Steps

Evaluate

42 \times 4 2^{3}

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

4 2 \times 2^{3}

Calculate the product

4 2^{4}

Reduce the index of the radical and exponent with 4

2

\frac{4 24}{2}

x = \pm \frac{4 24}{2}

Separate the equation into 2 possible cases

x = \frac{4 24}{2} x = - \frac{4 24}{2}

Solution

x_{1} = - \frac{4 24}{2}, x_{2} = \frac{4 24}{2}

Alternative Form

x_{1} \approx - 1.106682, x_{2} \approx 1.106682

Show Solution