Solve -8t=-3(t^5) 10t

Question

Solve the equation

t_{1} = 0, t_{2} = \frac{5 202500}{15}

Alternative Form

t_{1} = 0, t_{2} \approx 0.767704

Evaluate

- 8 t = - 3 t^{5} \times 10 t

Multiply

More Steps

Evaluate

- 3 t^{5} \times 10 t

Multiply the terms

- 30 t^{5} \times t

Multiply the terms with the same base by adding their exponents

- 30 t^{5 + 1}

Add the numbers

- 30 t^{6}

- 8 t = - 30 t^{6}

Add or subtract both sides

- 8 t - (- 30 t^{6}) = 0

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

- 8 t + 30 t^{6} = 0

Factor the expression

2 t (- 4 + 15 t^{5}) = 0

Divide both sides

t (- 4 + 15 t^{5}) = 0

Separate the equation into 2 possible cases

t = 0 - 4 + 15 t^{5} = 0

Solve the equation

More Steps

Evaluate

- 4 + 15 t^{5} = 0

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

15 t^{5} = 0 + 4

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

15 t^{5} = 4

Divide both sides

\frac{15 t ^{5}}{15} = \frac{4}{15}

Divide the numbers

t^{5} = \frac{4}{15}

Take the 5 -th root on both sides of the equation

5 t^{5} = 5 \frac{4}{15}

Calculate

t = 5 \frac{4}{15}

Simplify the root

More Steps

Evaluate

5 \frac{4}{15}

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

\frac{5 4}{5 15}

Multiply by the Conjugate

\frac{5 4 \times 5 1 5 ^{4}}{5 15 \times 5 1 5 ^{4}}

Simplify

\frac{5 4 \times 5 50625}{5 15 \times 5 1 5 ^{4}}

Multiply the numbers

\frac{5 202500}{5 15 \times 5 1 5 ^{4}}

Multiply the numbers

\frac{5 202500}{15}

t = \frac{5 202500}{15}

t = 0 t = \frac{5 202500}{15}

Solution

t_{1} = 0, t_{2} = \frac{5 202500}{15}

Alternative Form

t_{1} = 0, t_{2} \approx 0.767704

Show Solution

Solve the equation

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