Solve 1111x^6666+7778x^3333

Question

Simplify the expression

739926 x^{6} + 2590074 x^{3}

Evaluate

1111 x^{6} \times 666 + 7778 x^{3} \times 333

Multiply the terms

739926 x^{6} + 7778 x^{3} \times 333

Solution

739926 x^{6} + 2590074 x^{3}

Show Solution

666 x^{3} (1111 x^{3} + 3889)

Evaluate

1111 x^{6} \times 666 + 7778 x^{3} \times 333

Multiply the terms

739926 x^{6} + 7778 x^{3} \times 333

Multiply the terms

739926 x^{6} + 2590074 x^{3}

Rewrite the expression

666 x^{3} \times 1111 x^{3} + 666 x^{3} \times 3889

Solution

666 x^{3} (1111 x^{3} + 3889)

Show Solution

x_{1} = - \frac{3 3889 \times 111 1 ^{2}}{1111}, x_{2} = 0

Alternative Form

x_{1} \approx - 1.51836, x_{2} = 0

Evaluate

1111 x^{6} \times 666 + 7778 x^{3} \times 333

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

1111 x^{6} \times 666 + 7778 x^{3} \times 333 = 0

Multiply the terms

739926 x^{6} + 7778 x^{3} \times 333 = 0

Multiply the terms

739926 x^{6} + 2590074 x^{3} = 0

Factor the expression

666 x^{3} (1111 x^{3} + 3889) = 0

Divide both sides

x^{3} (1111 x^{3} + 3889) = 0

Separate the equation into 2 possible cases

x^{3} = 0 1111 x^{3} + 3889 = 0

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

x = 0 1111 x^{3} + 3889 = 0

Solve the equation

More Steps

Evaluate

1111 x^{3} + 3889 = 0

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

1111 x^{3} = 0 - 3889

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

1111 x^{3} = - 3889

Divide both sides

\frac{1111 x ^{3}}{1111} = \frac{- 3889}{1111}

Divide the numbers

x^{3} = \frac{- 3889}{1111}

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

x^{3} = - \frac{3889}{1111}

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

3 x^{3} = 3 - \frac{3889}{1111}

Calculate

x = 3 - \frac{3889}{1111}

Simplify the root

More Steps

Evaluate

3 - \frac{3889}{1111}

An odd root of a negative radicand is always a negative

- 3 \frac{3889}{1111}

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

- \frac{3 3889}{3 1111}

Multiply by the Conjugate

\frac{- 3 3889 \times 3 111 1 ^{2}}{3 1111 \times 3 111 1 ^{2}}

The product of roots with the same index is equal to the root of the product

\frac{- 3 3889 \times 111 1 ^{2}}{3 1111 \times 3 111 1 ^{2}}

Multiply the numbers

\frac{- 3 3889 \times 111 1 ^{2}}{1111}

Calculate

- \frac{3 3889 \times 111 1 ^{2}}{1111}

x = - \frac{3 3889 \times 111 1 ^{2}}{1111}

x = 0 x = - \frac{3 3889 \times 111 1 ^{2}}{1111}

Solution

x_{1} = - \frac{3 3889 \times 111 1 ^{2}}{1111}, x_{2} = 0

Alternative Form

x_{1} \approx - 1.51836, x_{2} = 0

Show Solution