Solve 25x17x^432x^24+32x^26

Question

Simplify the expression

54400 x^{7} + 192 x^{2}

Evaluate

25 x \times 17 x^{4} \times 32 x^{2} \times 4 + 32 x^{2} \times 6

Multiply

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Multiply the terms

25 x \times 17 x^{4} \times 32 x^{2} \times 4

Multiply the terms

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Evaluate

25 \times 17 \times 32 \times 4

Multiply the terms

425 \times 32 \times 4

Multiply the terms

13600 \times 4

Multiply the numbers

54400

54400 x \times x^{4} \times x^{2}

Multiply the terms with the same base by adding their exponents

54400 x^{1 + 4 + 2}

Add the numbers

54400 x^{7}

54400 x^{7} + 32 x^{2} \times 6

Solution

54400 x^{7} + 192 x^{2}

Show Solution

Factor the expression

64 x^{2} (850 x^{5} + 3)

Evaluate

25 x \times 17 x^{4} \times 32 x^{2} \times 4 + 32 x^{2} \times 6

Multiply

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Multiply the terms

25 x \times 17 x^{4} \times 32 x^{2} \times 4

Multiply the terms

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Evaluate

25 \times 17 \times 32 \times 4

Multiply the terms

425 \times 32 \times 4

Multiply the terms

13600 \times 4

Multiply the numbers

54400

54400 x \times x^{4} \times x^{2}

Multiply the terms with the same base by adding their exponents

54400 x^{1 + 4 + 2}

Add the numbers

54400 x^{7}

54400 x^{7} + 32 x^{2} \times 6

Multiply the terms

54400 x^{7} + 192 x^{2}

Rewrite the expression

64 x^{2} \times 850 x^{5} + 64 x^{2} \times 3

Solution

64 x^{2} (850 x^{5} + 3)

Show Solution

Find the roots

x_{1} = - \frac{5 3 \times 85 0 ^{4}}{850}, x_{2} = 0

Alternative Form

x_{1} \approx - 0.323251, x_{2} = 0

Evaluate

25 x \times 17 x^{4} \times 32 x^{2} \times 4 + 32 x^{2} \times 6

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

25 x \times 17 x^{4} \times 32 x^{2} \times 4 + 32 x^{2} \times 6 = 0

Multiply

More Steps

Multiply the terms

25 x \times 17 x^{4} \times 32 x^{2} \times 4

Multiply the terms

More Steps

Evaluate

25 \times 17 \times 32 \times 4

Multiply the terms

425 \times 32 \times 4

Multiply the terms

13600 \times 4

Multiply the numbers

54400

54400 x \times x^{4} \times x^{2}

Multiply the terms with the same base by adding their exponents

54400 x^{1 + 4 + 2}

Add the numbers

54400 x^{7}

54400 x^{7} + 32 x^{2} \times 6 = 0

Multiply the terms

54400 x^{7} + 192 x^{2} = 0

Factor the expression

64 x^{2} (850 x^{5} + 3) = 0

Divide both sides

x^{2} (850 x^{5} + 3) = 0

Separate the equation into 2 possible cases

x^{2} = 0 850 x^{5} + 3 = 0

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

x = 0 850 x^{5} + 3 = 0

Solve the equation

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Evaluate

850 x^{5} + 3 = 0

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

850 x^{5} = 0 - 3

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

850 x^{5} = - 3

Divide both sides

\frac{850 x ^{5}}{850} = \frac{- 3}{850}

Divide the numbers

x^{5} = \frac{- 3}{850}

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

x^{5} = - \frac{3}{850}

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

5 x^{5} = 5 - \frac{3}{850}

Calculate

x = 5 - \frac{3}{850}

Simplify the root

More Steps

Evaluate

5 - \frac{3}{850}

An odd root of a negative radicand is always a negative

- 5 \frac{3}{850}

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

- \frac{5 3}{5 850}

Multiply by the Conjugate

\frac{- 5 3 \times 5 85 0 ^{4}}{5 850 \times 5 85 0 ^{4}}

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

\frac{- 5 3 \times 85 0 ^{4}}{5 850 \times 5 85 0 ^{4}}

Multiply the numbers

\frac{- 5 3 \times 85 0 ^{4}}{850}

Calculate

- \frac{5 3 \times 85 0 ^{4}}{850}

x = - \frac{5 3 \times 85 0 ^{4}}{850}

x = 0 x = - \frac{5 3 \times 85 0 ^{4}}{850}

Solution

x_{1} = - \frac{5 3 \times 85 0 ^{4}}{850}, x_{2} = 0

Alternative Form

x_{1} \approx - 0.323251, x_{2} = 0

Show Solution