Solve x^25x-14x^212x^35

Question

Simplify the expression

5 x^{3} - 840 x^{5}

Evaluate

x^{2} \times 5 x - 14 x^{2} \times 12 x^{3} \times 5

Multiply

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Multiply the terms

x^{2} \times 5 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 5

Add the numbers

x^{3} \times 5

Use the commutative property to reorder the terms

5 x^{3}

5 x^{3} - 14 x^{2} \times 12 x^{3} \times 5

Solution

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Multiply the terms

14 x^{2} \times 12 x^{3} \times 5

Multiply the terms

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Evaluate

14 \times 12 \times 5

Multiply the terms

168 \times 5

Multiply the numbers

840

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

Multiply the terms with the same base by adding their exponents

840 x^{2 + 3}

Add the numbers

840 x^{5}

5 x^{3} - 840 x^{5}

Show Solution

Factor the expression

5 x^{3} (1 - 168 x^{2})

Evaluate

x^{2} \times 5 x - 14 x^{2} \times 12 x^{3} \times 5

Multiply

More Steps

Multiply the terms

x^{2} \times 5 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 5

Add the numbers

x^{3} \times 5

Use the commutative property to reorder the terms

5 x^{3}

5 x^{3} - 14 x^{2} \times 12 x^{3} \times 5

Multiply

More Steps

Multiply the terms

14 x^{2} \times 12 x^{3} \times 5

Multiply the terms

More Steps

Evaluate

14 \times 12 \times 5

Multiply the terms

168 \times 5

Multiply the numbers

840

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

Multiply the terms with the same base by adding their exponents

840 x^{2 + 3}

Add the numbers

840 x^{5}

5 x^{3} - 840 x^{5}

Rewrite the expression

5 x^{3} - 5 x^{3} \times 168 x^{2}

Solution

5 x^{3} (1 - 168 x^{2})

Show Solution

Find the roots

x_{1} = - \frac{42}{84}, x_{2} = 0, x_{3} = \frac{42}{84}

Alternative Form

x_{1} \approx - 0.077152, x_{2} = 0, x_{3} \approx 0.077152

Evaluate

x^{2} \times 5 x - 14 x^{2} \times 12 x^{3} \times 5

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

x^{2} \times 5 x - 14 x^{2} \times 12 x^{3} \times 5 = 0

Multiply

More Steps

Multiply the terms

x^{2} \times 5 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 5

Add the numbers

x^{3} \times 5

Use the commutative property to reorder the terms

5 x^{3}

5 x^{3} - 14 x^{2} \times 12 x^{3} \times 5 = 0

Multiply

More Steps

Multiply the terms

14 x^{2} \times 12 x^{3} \times 5

Multiply the terms

More Steps

Evaluate

14 \times 12 \times 5

Multiply the terms

168 \times 5

Multiply the numbers

840

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

Multiply the terms with the same base by adding their exponents

840 x^{2 + 3}

Add the numbers

840 x^{5}

5 x^{3} - 840 x^{5} = 0

Factor the expression

5 x^{3} (1 - 168 x^{2}) = 0

Divide both sides

x^{3} (1 - 168 x^{2}) = 0

Separate the equation into 2 possible cases

x^{3} = 0 1 - 168 x^{2} = 0

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

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

Solve the equation

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Evaluate

1 - 168 x^{2} = 0

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

- 168 x^{2} = 0 - 1

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

- 168 x^{2} = - 1

Change the signs on both sides of the equation

168 x^{2} = 1

Divide both sides

\frac{168 x ^{2}}{168} = \frac{1}{168}

Divide the numbers

x^{2} = \frac{1}{168}

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm \frac{1}{168}

Simplify the expression

More Steps

Evaluate

\frac{1}{168}

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

\frac{1}{168}

Simplify the radical expression

\frac{1}{168}

Simplify the radical expression

\frac{1}{2 42}

Multiply by the Conjugate

\frac{42}{2 42 \times 42}

Multiply the numbers

\frac{42}{84}

x = \pm \frac{42}{84}

Separate the equation into 2 possible cases

x = \frac{42}{84} x = - \frac{42}{84}

x = 0 x = \frac{42}{84} x = - \frac{42}{84}

Solution

x_{1} = - \frac{42}{84}, x_{2} = 0, x_{3} = \frac{42}{84}

Alternative Form

x_{1} \approx - 0.077152, x_{2} = 0, x_{3} \approx 0.077152

Show Solution