Solve q^43-1092-204

Question

Simplify the expression

3 q^{4} - 1296

Evaluate

q^{4} \times 3 - 1092 - 204

Use the commutative property to reorder the terms

3 q^{4} - 1092 - 204

Solution

3 q^{4} - 1296

Show Solution

3 (q^{4} - 432)

Evaluate

q^{4} \times 3 - 1092 - 204

Use the commutative property to reorder the terms

3 q^{4} - 1092 - 204

Subtract the numbers

3 q^{4} - 1296

Solution

3 (q^{4} - 432)

Show Solution

q_{1} = - 2427, q_{2} = 2427

Alternative Form

q_{1} \approx - 4.559014, q_{2} \approx 4.559014

Evaluate

q^{4} \times 3 - 1092 - 204

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

q^{4} \times 3 - 1092 - 204 = 0

Use the commutative property to reorder the terms

3 q^{4} - 1092 - 204 = 0

Subtract the numbers

3 q^{4} - 1296 = 0

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

3 q^{4} = 0 + 1296

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

3 q^{4} = 1296

Divide both sides

\frac{3 q ^{4}}{3} = \frac{1296}{3}

Divide the numbers

q^{4} = \frac{1296}{3}

Divide the numbers

More Steps

Evaluate

\frac{1296}{3}

Reduce the numbers

\frac{432}{1}

Calculate

432

q^{4} = 432

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

q = \pm 4432

Simplify the expression

More Steps

Evaluate

4432

Write the expression as a product where the root of one of the factors can be evaluated

4 16 \times 27

Write the number in exponential form with the base of 2

4 2^{4} \times 27

The root of a product is equal to the product of the roots of each factor

4 2^{4} \times 427

Reduce the index of the radical and exponent with 4

2427

q = \pm 2427

Separate the equation into 2 possible cases

q = 2427 q = - 2427

Solution

q_{1} = - 2427, q_{2} = 2427

Alternative Form

q_{1} \approx - 4.559014, q_{2} \approx 4.559014

Show Solution