Solve 30t^4-1975 - ScanMath

Question

Factor the expression

5 (6 t^{4} - 395)

Evaluate

30 t^{4} - 1975

Solution

5 (6 t^{4} - 395)

Show Solution

t_{1} = - \frac{4 85320}{6}, t_{2} = \frac{4 85320}{6}

Alternative Form

t_{1} \approx - 2.848469, t_{2} \approx 2.848469

Evaluate

30 t^{4} - 1975

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

30 t^{4} - 1975 = 0

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

30 t^{4} = 0 + 1975

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

30 t^{4} = 1975

Divide both sides

\frac{30 t ^{4}}{30} = \frac{1975}{30}

Divide the numbers

t^{4} = \frac{1975}{30}

Cancel out the common factor 5

t^{4} = \frac{395}{6}

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

t = \pm 4 \frac{395}{6}

Simplify the expression

More Steps

Evaluate

4 \frac{395}{6}

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

\frac{4 395}{4 6}

Multiply by the Conjugate

\frac{4 395 \times 4 6 ^{3}}{4 6 \times 4 6 ^{3}}

Simplify

\frac{4 395 \times 4 216}{4 6 \times 4 6 ^{3}}

Multiply the numbers

More Steps

Evaluate

4395 \times 4216

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

4 395 \times 216

Calculate the product

485320

\frac{4 85320}{4 6 \times 4 6 ^{3}}

Multiply the numbers

More Steps

Evaluate

46 \times 4 6^{3}

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

4 6 \times 6^{3}

Calculate the product

4 6^{4}

Reduce the index of the radical and exponent with 4

6

\frac{4 85320}{6}

t = \pm \frac{4 85320}{6}

Separate the equation into 2 possible cases

t = \frac{4 85320}{6} t = - \frac{4 85320}{6}

Solution

t_{1} = - \frac{4 85320}{6}, t_{2} = \frac{4 85320}{6}

Alternative Form

t_{1} \approx - 2.848469, t_{2} \approx 2.848469

Show Solution