Solve q^43-1092-205

Question

Simplify the expression

3 q^{4} - 1297

Evaluate

q^{4} \times 3 - 1092 - 205

Use the commutative property to reorder the terms

3 q^{4} - 1092 - 205

Solution

3 q^{4} - 1297

Show Solution

q_{1} = - \frac{4 35019}{3}, q_{2} = \frac{4 35019}{3}

Alternative Form

q_{1} \approx - 4.559893, q_{2} \approx 4.559893

Evaluate

q^{4} \times 3 - 1092 - 205

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

q^{4} \times 3 - 1092 - 205 = 0

Use the commutative property to reorder the terms

3 q^{4} - 1092 - 205 = 0

Subtract the numbers

3 q^{4} - 1297 = 0

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

3 q^{4} = 0 + 1297

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

3 q^{4} = 1297

Divide both sides

\frac{3 q ^{4}}{3} = \frac{1297}{3}

Divide the numbers

q^{4} = \frac{1297}{3}

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

q = \pm 4 \frac{1297}{3}

Simplify the expression

More Steps

Evaluate

4 \frac{1297}{3}

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

\frac{4 1297}{4 3}

Multiply by the Conjugate

\frac{4 1297 \times 4 3 ^{3}}{4 3 \times 4 3 ^{3}}

Simplify

\frac{4 1297 \times 4 27}{4 3 \times 4 3 ^{3}}

Multiply the numbers

More Steps

Evaluate

41297 \times 427

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

4 1297 \times 27

Calculate the product

435019

\frac{4 35019}{4 3 \times 4 3 ^{3}}

Multiply the numbers

More Steps

Evaluate

43 \times 4 3^{3}

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

4 3 \times 3^{3}

Calculate the product

4 3^{4}

Reduce the index of the radical and exponent with 4

3

\frac{4 35019}{3}

q = \pm \frac{4 35019}{3}

Separate the equation into 2 possible cases

q = \frac{4 35019}{3} q = - \frac{4 35019}{3}

Solution

q_{1} = - \frac{4 35019}{3}, q_{2} = \frac{4 35019}{3}

Alternative Form

q_{1} \approx - 4.559893, q_{2} \approx 4.559893

Show Solution