Solve -6x^24x^2x 7x^2 -x^2

Question

Simplify the expression

- 168 x^{7} - x^{2}

Evaluate

- 6 x^{2} \times 4 x^{2} \times x \times 7 x^{2} - x^{2}

Solution

More Steps

Evaluate

- 6 x^{2} \times 4 x^{2} \times x \times 7 x^{2}

Multiply the terms

More Steps

Evaluate

6 \times 4 \times 7

Multiply the terms

24 \times 7

Multiply the numbers

168

- 168 x^{2} \times x^{2} \times x \times x^{2}

Multiply the terms with the same base by adding their exponents

- 168 x^{2 + 2 + 1 + 2}

Add the numbers

- 168 x^{7}

- 168 x^{7} - x^{2}

Show Solution

Factor the expression

- x^{2} (168 x^{5} + 1)

Evaluate

- 6 x^{2} \times 4 x^{2} \times x \times 7 x^{2} - x^{2}

Multiply

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Evaluate

- 6 x^{2} \times 4 x^{2} \times x \times 7 x^{2}

Multiply the terms

More Steps

Evaluate

6 \times 4 \times 7

Multiply the terms

24 \times 7

Multiply the numbers

168

- 168 x^{2} \times x^{2} \times x \times x^{2}

Multiply the terms with the same base by adding their exponents

- 168 x^{2 + 2 + 1 + 2}

Add the numbers

- 168 x^{7}

- 168 x^{7} - x^{2}

Rewrite the expression

- x^{2} \times 168 x^{5} - x^{2}

Solution

- x^{2} (168 x^{5} + 1)

Show Solution

Find the roots

x_{1} = - \frac{5 16 8 ^{4}}{168}, x_{2} = 0

Alternative Form

x_{1} \approx - 0.358871, x_{2} = 0

Evaluate

- 6 x^{2} \times 4 x^{2} \times x \times 7 x^{2} - x^{2}

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

- 6 x^{2} \times 4 x^{2} \times x \times 7 x^{2} - x^{2} = 0

Multiply

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Multiply the terms

- 6 x^{2} \times 4 x^{2} \times x \times 7 x^{2}

Multiply the terms

More Steps

Evaluate

6 \times 4 \times 7

Multiply the terms

24 \times 7

Multiply the numbers

168

- 168 x^{2} \times x^{2} \times x \times x^{2}

Multiply the terms with the same base by adding their exponents

- 168 x^{2 + 2 + 1 + 2}

Add the numbers

- 168 x^{7}

- 168 x^{7} - x^{2} = 0

Factor the expression

- x^{2} (168 x^{5} + 1) = 0

Divide both sides

x^{2} (168 x^{5} + 1) = 0

Separate the equation into 2 possible cases

x^{2} = 0 168 x^{5} + 1 = 0

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

x = 0 168 x^{5} + 1 = 0

Solve the equation

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Evaluate

168 x^{5} + 1 = 0

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

168 x^{5} = 0 - 1

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

168 x^{5} = - 1

Divide both sides

\frac{168 x ^{5}}{168} = \frac{- 1}{168}

Divide the numbers

x^{5} = \frac{- 1}{168}

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

x^{5} = - \frac{1}{168}

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

5 x^{5} = 5 - \frac{1}{168}

Calculate

x = 5 - \frac{1}{168}

Simplify the root

More Steps

Evaluate

5 - \frac{1}{168}

An odd root of a negative radicand is always a negative

- 5 \frac{1}{168}

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

- \frac{5 1}{5 168}

Simplify the radical expression

- \frac{1}{5 168}

Multiply by the Conjugate

\frac{- 5 16 8 ^{4}}{5 168 \times 5 16 8 ^{4}}

Multiply the numbers

\frac{- 5 16 8 ^{4}}{168}

Calculate

- \frac{5 16 8 ^{4}}{168}

x = - \frac{5 16 8 ^{4}}{168}

x = 0 x = - \frac{5 16 8 ^{4}}{168}

Solution

x_{1} = - \frac{5 16 8 ^{4}}{168}, x_{2} = 0

Alternative Form

x_{1} \approx - 0.358871, x_{2} = 0

Show Solution