Solve -2t^2-9t^56

Question

Simplify the expression

- 2 t^{2} - 54 t^{5}

Evaluate

- 2 t^{2} - 9 t^{5} \times 6

Solution

- 2 t^{2} - 54 t^{5}

Show Solution

- 2 t^{2} (1 + 3 t) (1 - 3 t + 9 t^{2})

Evaluate

- 2 t^{2} - 9 t^{5} \times 6

Evaluate

- 2 t^{2} - 54 t^{5}

Factor out - 2 t^{2} from the expression

- 2 t^{2} (1 + 27 t^{3})

Solution

More Steps

Evaluate

1 + 27 t^{3}

Rewrite the expression in exponential form

1^{3} + (3 t)^{3}

Use a^{3} + b^{3} = (a + b) (a^{2} - ab + b^{2}) to factor the expression

(1 + 3 t) (1^{2} - 1 \times 3 t + (3 t)^{2})

1 raised to any power equals to 1

(1 + 3 t) (1 - 1 \times 3 t + (3 t)^{2})

Any expression multiplied by 1 remains the same

(1 + 3 t) (1 - 3 t + (3 t)^{2})

Evaluate

More Steps

Evaluate

(3 t)^{2}

To raise a product to a power,raise each factor to that power

3^{2} t^{2}

Evaluate the power

9 t^{2}

(1 + 3 t) (1 - 3 t + 9 t^{2})

- 2 t^{2} (1 + 3 t) (1 - 3 t + 9 t^{2})

Show Solution

t_{1} = - \frac{1}{3}, t_{2} = 0

Alternative Form

t_{1} = - 0. \dot{3}, t_{2} = 0

Evaluate

- 2 t^{2} - 9 t^{5} \times 6

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

- 2 t^{2} - 9 t^{5} \times 6 = 0

Multiply the terms

- 2 t^{2} - 54 t^{5} = 0

Factor the expression

- 2 t^{2} (1 + 27 t^{3}) = 0

Divide both sides

t^{2} (1 + 27 t^{3}) = 0

Separate the equation into 2 possible cases

t^{2} = 0 1 + 27 t^{3} = 0

The only way a power can be 0 is when the base equals 0

t = 0 1 + 27 t^{3} = 0

Solve the equation

More Steps

Evaluate

1 + 27 t^{3} = 0

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

27 t^{3} = 0 - 1

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

27 t^{3} = - 1

Divide both sides

\frac{27 t ^{3}}{27} = \frac{- 1}{27}

Divide the numbers

t^{3} = \frac{- 1}{27}

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

t^{3} = - \frac{1}{27}

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

3 t^{3} = 3 - \frac{1}{27}

Calculate

t = 3 - \frac{1}{27}

Simplify the root

More Steps

Evaluate

3 - \frac{1}{27}

An odd root of a negative radicand is always a negative

- 3 \frac{1}{27}

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

- \frac{3 1}{3 27}

Simplify the radical expression

- \frac{1}{3 27}

Simplify the radical expression

- \frac{1}{3}

t = - \frac{1}{3}

t = 0 t = - \frac{1}{3}

Solution

t_{1} = - \frac{1}{3}, t_{2} = 0

Alternative Form

t_{1} = - 0. \dot{3}, t_{2} = 0

Show Solution