Solve (x^24) (3x^24)=180

Question

Solve the equation

x_{1} = - \frac{4 60}{2}, x_{2} = \frac{4 60}{2}

Alternative Form

x_{1} \approx - 1.391579, x_{2} \approx 1.391579

Evaluate

(x^{2} \times 4) (3 x^{2} \times 4) = 180

Remove the parentheses

x^{2} \times 4 \times 3 x^{2} \times 4 = 180

Multiply

More Steps

Evaluate

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

Multiply the terms with the same base by adding their exponents

x^{2 + 2} \times 4 \times 3 \times 4

Add the numbers

x^{4} \times 4 \times 3 \times 4

Multiply the terms

More Steps

Evaluate

4 \times 3 \times 4

Multiply the terms

12 \times 4

Multiply the numbers

48

x^{4} \times 48

Use the commutative property to reorder the terms

48 x^{4}

48 x^{4} = 180

Divide both sides

\frac{48 x ^{4}}{48} = \frac{180}{48}

Divide the numbers

x^{4} = \frac{180}{48}

Cancel out the common factor 12

x^{4} = \frac{15}{4}

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

x = \pm 4 \frac{15}{4}

Simplify the expression

More Steps

Evaluate

4 \frac{15}{4}

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

\frac{4 15}{4 4}

Simplify the radical expression

More Steps

Evaluate

44

Write the number in exponential form with the base of 2

4 2^{2}

Reduce the index of the radical and exponent with 2

2

\frac{4 15}{2}

Multiply by the Conjugate

\frac{4 15 \times 2}{2 \times 2}

Multiply the numbers

More Steps

Evaluate

415 \times 2

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

415 \times 4 2^{2}

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

4 15 \times 2^{2}

Calculate the product

460

\frac{4 60}{2 \times 2}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{4 60}{2}

x = \pm \frac{4 60}{2}

Separate the equation into 2 possible cases

x = \frac{4 60}{2} x = - \frac{4 60}{2}

Solution

x_{1} = - \frac{4 60}{2}, x_{2} = \frac{4 60}{2}

Alternative Form

x_{1} \approx - 1.391579, x_{2} \approx 1.391579

Show Solution