Solve x^2(5x^23)-17x(5x^23) 70(5x^23)

Question

Simplify the expression

15 x^{4} - 267750 x^{5}

Evaluate

x^{2} (5 x^{2} \times 3) - 17 x (5 x^{2} \times 3) \times 70 (5 x^{2} \times 3)

Remove the parentheses

x^{2} \times 5 x^{2} \times 3 - 17 x \times 5 x^{2} \times 3 \times 70 \times 5 x^{2} \times 3

Multiply

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Multiply the terms

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

Multiply the terms with the same base by adding their exponents

x^{2 + 2} \times 5 \times 3

Add the numbers

x^{4} \times 5 \times 3

Multiply the terms

x^{4} \times 15

Use the commutative property to reorder the terms

15 x^{4}

15 x^{4} - 17 x \times 5 x^{2} \times 3 \times 70 \times 5 x^{2} \times 3

Solution

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Multiply the terms

17 x \times 5 x^{2} \times 3 \times 70 \times 5 x^{2} \times 3

Multiply the terms

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Evaluate

17 \times 5 \times 3 \times 70 \times 5 \times 3

Multiply the terms

85 \times 3 \times 70 \times 5 \times 3

Multiply the terms

255 \times 70 \times 5 \times 3

Multiply the terms

17850 \times 5 \times 3

Multiply the terms

89250 \times 3

Multiply the numbers

267750

267750 x \times x^{2} \times x^{2}

Multiply the terms with the same base by adding their exponents

267750 x^{1 + 2 + 2}

Add the numbers

267750 x^{5}

15 x^{4} - 267750 x^{5}

Show Solution

Factor the expression

15 x^{4} (1 - 17850 x)

Evaluate

x^{2} (5 x^{2} \times 3) - 17 x (5 x^{2} \times 3) \times 70 (5 x^{2} \times 3)

Remove the parentheses

x^{2} \times 5 x^{2} \times 3 - 17 x \times 5 x^{2} \times 3 \times 70 \times 5 x^{2} \times 3

Multiply the terms

x^{2} \times 15 x^{2} - 17 x \times 5 x^{2} \times 3 \times 70 \times 5 x^{2} \times 3

Multiply the terms

More Steps

Evaluate

x^{2} \times 15 x^{2}

Use the commutative property to reorder the terms

15 x^{2} \times x^{2}

Multiply the terms

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Evaluate

x^{2} \times x^{2}

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

x^{2 + 2}

Add the numbers

x^{4}

15 x^{4}

15 x^{4} - 17 x \times 5 x^{2} \times 3 \times 70 \times 5 x^{2} \times 3

Multiply the terms

15 x^{4} - 17 x \times 15 x^{2} \times 70 \times 5 x^{2} \times 3

Multiply the terms

15 x^{4} - 17 x \times 15 x^{2} \times 70 \times 15 x^{2}

Multiply

More Steps

Multiply the terms

17 x \times 15 x^{2} \times 70 \times 15 x^{2}

Multiply the terms

More Steps

Evaluate

17 \times 15 \times 70 \times 15

Multiply the terms

255 \times 70 \times 15

Multiply the terms

17850 \times 15

Multiply the numbers

267750

267750 x \times x^{2} \times x^{2}

Multiply the terms with the same base by adding their exponents

267750 x^{1 + 2 + 2}

Add the numbers

267750 x^{5}

15 x^{4} - 267750 x^{5}

Rewrite the expression

15 x^{4} - 15 x^{4} \times 17850 x

Solution

15 x^{4} (1 - 17850 x)

Show Solution

Find the roots

x_{1} = 0, x_{2} = \frac{1}{17850}

Alternative Form

x_{1} = 0, x_{2} \approx 5.602241 \times 1 0^{- 5}

Evaluate

x^{2} (5 x^{2} \times 3) - 17 x (5 x^{2} \times 3) \times 70 (5 x^{2} \times 3)

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

x^{2} (5 x^{2} \times 3) - 17 x (5 x^{2} \times 3) \times 70 (5 x^{2} \times 3) = 0

Multiply the terms

x^{2} \times 15 x^{2} - 17 x (5 x^{2} \times 3) \times 70 (5 x^{2} \times 3) = 0

Multiply the terms

x^{2} \times 15 x^{2} - 17 x \times 15 x^{2} \times 70 (5 x^{2} \times 3) = 0

Multiply the terms

x^{2} \times 15 x^{2} - 17 x \times 15 x^{2} \times 70 \times 15 x^{2} = 0

Multiply the terms

More Steps

Evaluate

x^{2} \times 15 x^{2}

Use the commutative property to reorder the terms

15 x^{2} \times x^{2}

Multiply the terms

More Steps

Evaluate

x^{2} \times x^{2}

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

x^{2 + 2}

Add the numbers

x^{4}

15 x^{4}

15 x^{4} - 17 x \times 15 x^{2} \times 70 \times 15 x^{2} = 0

Multiply

More Steps

Multiply the terms

17 x \times 15 x^{2} \times 70 \times 15 x^{2}

Multiply the terms

More Steps

Evaluate

17 \times 15 \times 70 \times 15

Multiply the terms

255 \times 70 \times 15

Multiply the terms

17850 \times 15

Multiply the numbers

267750

267750 x \times x^{2} \times x^{2}

Multiply the terms with the same base by adding their exponents

267750 x^{1 + 2 + 2}

Add the numbers

267750 x^{5}

15 x^{4} - 267750 x^{5} = 0

Factor the expression

15 x^{4} (1 - 17850 x) = 0

Divide both sides

x^{4} (1 - 17850 x) = 0

Separate the equation into 2 possible cases

x^{4} = 0 1 - 17850 x = 0

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

x = 0 1 - 17850 x = 0

Solve the equation

More Steps

Evaluate

1 - 17850 x = 0

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

- 17850 x = 0 - 1

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

- 17850 x = - 1

Change the signs on both sides of the equation

17850 x = 1

Divide both sides

\frac{17850 x}{17850} = \frac{1}{17850}

Divide the numbers

x = \frac{1}{17850}

x = 0 x = \frac{1}{17850}

Solution

x_{1} = 0, x_{2} = \frac{1}{17850}

Alternative Form

x_{1} = 0, x_{2} \approx 5.602241 \times 1 0^{- 5}

Show Solution