Solve a+1(a^91-a^98-a^99-a-1)

Question

Simplify the expression

- 16 a^{9} - 1

Show Solution

a = - \frac{9 32}{2}

Alternative Form

a \approx - 0.734867

Evaluate

a + 1 \times (a^{9} \times 1 - a^{9} \times 8 - a^{9} \times 9 - a - 1)

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

a + 1 \times (a^{9} \times 1 - a^{9} \times 8 - a^{9} \times 9 - a - 1) = 0

Any expression multiplied by 1 remains the same

a + 1 \times (a^{9} - a^{9} \times 8 - a^{9} \times 9 - a - 1) = 0

Use the commutative property to reorder the terms

a + 1 \times (a^{9} - 8 a^{9} - a^{9} \times 9 - a - 1) = 0

Use the commutative property to reorder the terms

a + 1 \times (a^{9} - 8 a^{9} - 9 a^{9} - a - 1) = 0

Subtract the terms

More Steps

a + 1 \times (- 7 a^{9} - 9 a^{9} - a - 1) = 0

Subtract the terms

More Steps

a + 1 \times (- 16 a^{9} - a - 1) = 0

Any expression multiplied by 1 remains the same

a - 16 a^{9} - a - 1 = 0

Subtract the terms

More Steps

- 16 a^{9} - 1 = 0

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

- 16 a^{9} = 0 + 1

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

- 16 a^{9} = 1

Change the signs on both sides of the equation

16 a^{9} = - 1

Divide both sides

\frac{16 a ^{9}}{16} = \frac{- 1}{16}

Divide the numbers

a^{9} = \frac{- 1}{16}

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

a^{9} = - \frac{1}{16}

Take the 9 -th root on both sides of the equation

9 a^{9} = 9 - \frac{1}{16}

Calculate

a = 9 - \frac{1}{16}

Solution

More Steps

a = - \frac{9 32}{2}

Alternative Form

a \approx - 0.734867

Show Solution