Solve 6a 12a^3=180

Question

Solve the equation

a_{1} = - \frac{4 40}{2}, a_{2} = \frac{4 40}{2}

Alternative Form

a_{1} \approx - 1.257433, a_{2} \approx 1.257433

Evaluate

6 a \times 12 a^{3} = 180

Multiply

More Steps

Evaluate

6 a \times 12 a^{3}

Multiply the terms

72 a \times a^{3}

Multiply the terms with the same base by adding their exponents

72 a^{1 + 3}

Add the numbers

72 a^{4}

72 a^{4} = 180

Divide both sides

\frac{72 a ^{4}}{72} = \frac{180}{72}

Divide the numbers

a^{4} = \frac{180}{72}

Cancel out the common factor 36

a^{4} = \frac{5}{2}

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

a = \pm 4 \frac{5}{2}

Simplify the expression

More Steps

Evaluate

4 \frac{5}{2}

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

\frac{4 5}{4 2}

Multiply by the Conjugate

\frac{4 5 \times 4 2 ^{3}}{4 2 \times 4 2 ^{3}}

Simplify

\frac{4 5 \times 4 8}{4 2 \times 4 2 ^{3}}

Multiply the numbers

More Steps

Evaluate

45 \times 48

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

4 5 \times 8

Calculate the product

440

\frac{4 40}{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 40}{2}

a = \pm \frac{4 40}{2}

Separate the equation into 2 possible cases

a = \frac{4 40}{2} a = - \frac{4 40}{2}

Solution

a_{1} = - \frac{4 40}{2}, a_{2} = \frac{4 40}{2}

Alternative Form

a_{1} \approx - 1.257433, a_{2} \approx 1.257433

Show Solution