Solve x^2-12x^27x^32x^2

Question

Simplify the expression

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

Evaluate

x^{2} - 12 x^{2} \times 7 x^{3} \times 2 x^{2}

Solution

More Steps

Evaluate

12 x^{2} \times 7 x^{3} \times 2 x^{2}

Multiply the terms

More Steps

Evaluate

12 \times 7 \times 2

Multiply the terms

84 \times 2

Multiply the numbers

168

168 x^{2} \times x^{3} \times x^{2}

Multiply the terms with the same base by adding their exponents

168 x^{2 + 3 + 2}

Add the numbers

168 x^{7}

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

Show Solution

Factor the expression

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

Evaluate

x^{2} - 12 x^{2} \times 7 x^{3} \times 2 x^{2}

Multiply

More Steps

Evaluate

12 x^{2} \times 7 x^{3} \times 2 x^{2}

Multiply the terms

More Steps

Evaluate

12 \times 7 \times 2

Multiply the terms

84 \times 2

Multiply the numbers

168

168 x^{2} \times x^{3} \times x^{2}

Multiply the terms with the same base by adding their exponents

168 x^{2 + 3 + 2}

Add the numbers

168 x^{7}

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

Rewrite the expression

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

Solution

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

Show Solution

Find the roots

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

Alternative Form

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

Evaluate

x^{2} - 12 x^{2} \times 7 x^{3} \times 2 x^{2}

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

x^{2} - 12 x^{2} \times 7 x^{3} \times 2 x^{2} = 0

Multiply

More Steps

Multiply the terms

12 x^{2} \times 7 x^{3} \times 2 x^{2}

Multiply the terms

More Steps

Evaluate

12 \times 7 \times 2

Multiply the terms

84 \times 2

Multiply the numbers

168

168 x^{2} \times x^{3} \times x^{2}

Multiply the terms with the same base by adding their exponents

168 x^{2 + 3 + 2}

Add the numbers

168 x^{7}

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

Factor the expression

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

Separate the equation into 2 possible cases

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

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

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

Solve the equation

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Evaluate

1 - 168 x^{5} = 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

Change the signs on both sides of the equation

168 x^{5} = 1

Divide both sides

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

Divide the numbers

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}

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}

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

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

Solution

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

Alternative Form

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

Show Solution