Solve 20t^296t-20

Question

20 t^{2} \times 96 t - 20

Simplify the expression

1920 t^{3} - 20

Evaluate

20 t^{2} \times 96 t - 20

Solution

More Steps

Evaluate

20 t^{2} \times 96 t

Multiply the terms

1920 t^{2} \times t

Multiply the terms with the same base by adding their exponents

1920 t^{2 + 1}

Add the numbers

1920 t^{3}

1920 t^{3} - 20

Show Solution

Factor the expression

20 (96 t^{3} - 1)

Evaluate

20 t^{2} \times 96 t - 20

Multiply

More Steps

Evaluate

20 t^{2} \times 96 t

Multiply the terms

1920 t^{2} \times t

Multiply the terms with the same base by adding their exponents

1920 t^{2 + 1}

Add the numbers

1920 t^{3}

1920 t^{3} - 20

Solution

20 (96 t^{3} - 1)

Show Solution

Find the roots

t = \frac{3 18}{12}

Alternative Form

t \approx 0.218395

Evaluate

20 t^{2} \times 96 t - 20

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

20 t^{2} \times 96 t - 20 = 0

Multiply

More Steps

Multiply the terms

20 t^{2} \times 96 t

Multiply the terms

1920 t^{2} \times t

Multiply the terms with the same base by adding their exponents

1920 t^{2 + 1}

Add the numbers

1920 t^{3}

1920 t^{3} - 20 = 0

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

1920 t^{3} = 0 + 20

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

1920 t^{3} = 20

Divide both sides

\frac{1920 t ^{3}}{1920} = \frac{20}{1920}

Divide the numbers

t^{3} = \frac{20}{1920}

Cancel out the common factor 20

t^{3} = \frac{1}{96}

Take the 3 -th root on both sides of the equation

3 t^{3} = 3 \frac{1}{96}

Calculate

t = 3 \frac{1}{96}

Solution

More Steps

Evaluate

3 \frac{1}{96}

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

\frac{3 1}{3 96}

Simplify the radical expression

\frac{1}{3 96}

Simplify the radical expression

More Steps

Evaluate

396

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

3 8 \times 12

Write the number in exponential form with the base of 2

3 2^{3} \times 12

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

3 2^{3} \times 312

Reduce the index of the radical and exponent with 3

2312

\frac{1}{2 3 12}

Multiply by the Conjugate

\frac{3 1 2 ^{2}}{2 3 12 \times 3 1 2 ^{2}}

Simplify

\frac{2 3 18}{2 3 12 \times 3 1 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

2312 \times 3 1 2^{2}

Multiply the terms

2 \times 12

Multiply the terms

24

\frac{2 3 18}{24}

Cancel out the common factor 2

\frac{3 18}{12}

t = \frac{3 18}{12}

Alternative Form

t \approx 0.218395

Show Solution