Solve t: 150=-16t^2 128t^6

Question

Solve the equation

t_{1} = - \frac{7 240 0 ^{6}}{4800}, t_{2} = 0

Alternative Form

t_{1} \approx - 0.164468, t_{2} = 0

Evaluate

t \div 150 = - 16 t^{2} \times 128 t^{6}

Rewrite the expression

\frac{t}{150} = - 16 t^{2} \times 128 t^{6}

Multiply

More Steps

Evaluate

- 16 t^{2} \times 128 t^{6}

Multiply the terms

- 2048 t^{2} \times t^{6}

Multiply the terms with the same base by adding their exponents

- 2048 t^{2 + 6}

Add the numbers

- 2048 t^{8}

\frac{t}{150} = - 2048 t^{8}

Cross multiply

t = 150 (- 2048 t^{8})

Simplify the equation

t = - 307200 t^{8}

Add or subtract both sides

t - (- 307200 t^{8}) = 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

t + 307200 t^{8} = 0

Factor the expression

t (1 + 307200 t^{7}) = 0

Separate the equation into 2 possible cases

t = 0 1 + 307200 t^{7} = 0

Solve the equation

More Steps

Evaluate

1 + 307200 t^{7} = 0

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

307200 t^{7} = 0 - 1

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

307200 t^{7} = - 1

Divide both sides

\frac{307200 t ^{7}}{307200} = \frac{- 1}{307200}

Divide the numbers

t^{7} = \frac{- 1}{307200}

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

t^{7} = - \frac{1}{307200}

Take the 7 -th root on both sides of the equation

7 t^{7} = 7 - \frac{1}{307200}

Calculate

t = 7 - \frac{1}{307200}

Simplify the root

More Steps

Evaluate

7 - \frac{1}{307200}

An odd root of a negative radicand is always a negative

- 7 \frac{1}{307200}

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

- \frac{7 1}{7 307200}

Simplify the radical expression

- \frac{1}{7 307200}

Simplify the radical expression

- \frac{1}{2 7 2400}

Multiply by the Conjugate

\frac{- 7 240 0 ^{6}}{2 7 2400 \times 7 240 0 ^{6}}

Multiply the numbers

\frac{- 7 240 0 ^{6}}{4800}

Calculate

- \frac{7 240 0 ^{6}}{4800}

t = - \frac{7 240 0 ^{6}}{4800}

t = 0 t = - \frac{7 240 0 ^{6}}{4800}

Solution

t_{1} = - \frac{7 240 0 ^{6}}{4800}, t_{2} = 0

Alternative Form

t_{1} \approx - 0.164468, t_{2} = 0

Show Solution

Solve the equation

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