Solve -16t^2 60t-40 - Socratic AI (ScanMath)

Question

Simplify the expression

- 960 t^{3} - 40

Evaluate

- 16 t^{2} \times 60 t - 40

Solution

More Steps

Evaluate

- 16 t^{2} \times 60 t

Multiply the terms

- 960 t^{2} \times t

Multiply the terms with the same base by adding their exponents

- 960 t^{2 + 1}

Add the numbers

- 960 t^{3}

- 960 t^{3} - 40

Show Solution

Factor the expression

- 40 (24 t^{3} + 1)

Evaluate

- 16 t^{2} \times 60 t - 40

Multiply

More Steps

Evaluate

- 16 t^{2} \times 60 t

Multiply the terms

- 960 t^{2} \times t

Multiply the terms with the same base by adding their exponents

- 960 t^{2 + 1}

Add the numbers

- 960 t^{3}

- 960 t^{3} - 40

Solution

- 40 (24 t^{3} + 1)

Show Solution

Find the roots

t = - \frac{3 9}{6}

Alternative Form

t \approx - 0.346681

Evaluate

- 16 t^{2} \times 60 t - 40

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

- 16 t^{2} \times 60 t - 40 = 0

Multiply

More Steps

Multiply the terms

- 16 t^{2} \times 60 t

Multiply the terms

- 960 t^{2} \times t

Multiply the terms with the same base by adding their exponents

- 960 t^{2 + 1}

Add the numbers

- 960 t^{3}

- 960 t^{3} - 40 = 0

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

- 960 t^{3} = 0 + 40

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

- 960 t^{3} = 40

Change the signs on both sides of the equation

960 t^{3} = - 40

Divide both sides

\frac{960 t ^{3}}{960} = \frac{- 40}{960}

Divide the numbers

t^{3} = \frac{- 40}{960}

Divide the numbers

More Steps

Evaluate

\frac{- 40}{960}

Cancel out the common factor 40

\frac{- 1}{24}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

- \frac{1}{24}

t^{3} = - \frac{1}{24}

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

3 t^{3} = 3 - \frac{1}{24}

Calculate

t = 3 - \frac{1}{24}

Solution

More Steps

Evaluate

3 - \frac{1}{24}

An odd root of a negative radicand is always a negative

- 3 \frac{1}{24}

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

- \frac{3 1}{3 24}

Simplify the radical expression

- \frac{1}{3 24}

Simplify the radical expression

More Steps

Evaluate

324

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

3 8 \times 3

Write the number in exponential form with the base of 2

3 2^{3} \times 3

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

3 2^{3} \times 33

Reduce the index of the radical and exponent with 3

233

- \frac{1}{2 3 3}

Rewrite the expression

\frac{- 1}{2 3 3}

Multiply by the Conjugate

\frac{- 3 3 ^{2}}{2 3 3 \times 3 3 ^{2}}

Simplify

\frac{- 3 9}{2 3 3 \times 3 3 ^{2}}

Multiply the numbers

More Steps

Evaluate

233 \times 3 3^{2}

Multiply the terms

2 \times 3

Multiply the terms

6

\frac{- 3 9}{6}

Calculate

- \frac{3 9}{6}

t = - \frac{3 9}{6}

Alternative Form

t \approx - 0.346681

Show Solution

16t^2 60t 40

Simplify the expression

Factor the expression

Find the roots