Solve (x^2-5x 7)(x^25x-7)

Question

Simplify the expression

5 x^{5} - 7 x^{2} - 175 x^{4} + 245 x

Evaluate

(x^{2} - 5 x \times 7) (x^{2} \times 5 x - 7)

Multiply the terms

(x^{2} - 35 x) (x^{2} \times 5 x - 7)

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}

(x^{2} - 35 x) (5 x^{3} - 7)

Apply the distributive property

x^{2} \times 5 x^{3} - x^{2} \times 7 - 35 x \times 5 x^{3} - (- 35 x \times 7)

Multiply the terms

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Evaluate

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

Use the commutative property to reorder the terms

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

Multiply the terms

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Evaluate

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

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

x^{2 + 3}

Add the numbers

x^{5}

5 x^{5}

5 x^{5} - x^{2} \times 7 - 35 x \times 5 x^{3} - (- 35 x \times 7)

Use the commutative property to reorder the terms

5 x^{5} - 7 x^{2} - 35 x \times 5 x^{3} - (- 35 x \times 7)

Multiply the terms

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Evaluate

- 35 x \times 5 x^{3}

Multiply the numbers

- 175 x \times x^{3}

Multiply the terms

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Evaluate

x \times x^{3}

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

x^{1 + 3}

Add the numbers

x^{4}

- 175 x^{4}

5 x^{5} - 7 x^{2} - 175 x^{4} - (- 35 x \times 7)

Multiply the numbers

5 x^{5} - 7 x^{2} - 175 x^{4} - (- 245 x)

Solution

5 x^{5} - 7 x^{2} - 175 x^{4} + 245 x

Show Solution

Factor the expression

x (x - 35) (5 x^{3} - 7)

Evaluate

(x^{2} - 5 x \times 7) (x^{2} \times 5 x - 7)

Multiply the terms

(x^{2} - 35 x) (x^{2} \times 5 x - 7)

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}

(x^{2} - 35 x) (5 x^{3} - 7)

Solution

More Steps

Evaluate

x^{2} - 35 x

Rewrite the expression

x \times x - x \times 35

Factor out x from the expression

x (x - 35)

x (x - 35) (5 x^{3} - 7)

Show Solution

Find the roots

x_{1} = 0, x_{2} = \frac{3 175}{5}, x_{3} = 35

Alternative Form

x_{1} = 0, x_{2} \approx 1.118689, x_{3} = 35

Evaluate

(x^{2} - 5 x \times 7) (x^{2} \times 5 x - 7)

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

(x^{2} - 5 x \times 7) (x^{2} \times 5 x - 7) = 0

Multiply the terms

(x^{2} - 35 x) (x^{2} \times 5 x - 7) = 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}

(x^{2} - 35 x) (5 x^{3} - 7) = 0

Separate the equation into 2 possible cases

x^{2} - 35 x = 0 5 x^{3} - 7 = 0

Solve the equation

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Evaluate

x^{2} - 35 x = 0

Factor the expression

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Evaluate

x^{2} - 35 x

Rewrite the expression

x \times x - x \times 35

Factor out x from the expression

x (x - 35)

x (x - 35) = 0

When the product of factors equals 0,at least one factor is 0

x = 0 x - 35 = 0

Solve the equation for x

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Evaluate

x - 35 = 0

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

x = 0 + 35

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

x = 35

x = 0 x = 35

x = 0 x = 35 5 x^{3} - 7 = 0

Solve the equation

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Evaluate

5 x^{3} - 7 = 0

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

5 x^{3} = 0 + 7

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

5 x^{3} = 7

Divide both sides

\frac{5 x ^{3}}{5} = \frac{7}{5}

Divide the numbers

x^{3} = \frac{7}{5}

Take the 3 -th root on both sides of the equation

3 x^{3} = 3 \frac{7}{5}

Calculate

x = 3 \frac{7}{5}

Simplify the root

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Evaluate

3 \frac{7}{5}

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

\frac{3 7}{3 5}

Multiply by the Conjugate

\frac{3 7 \times 3 5 ^{2}}{3 5 \times 3 5 ^{2}}

Simplify

\frac{3 7 \times 3 25}{3 5 \times 3 5 ^{2}}

Multiply the numbers

\frac{3 175}{3 5 \times 3 5 ^{2}}

Multiply the numbers

\frac{3 175}{5}

x = \frac{3 175}{5}

x = 0 x = 35 x = \frac{3 175}{5}

Solution

x_{1} = 0, x_{2} = \frac{3 175}{5}, x_{3} = 35

Alternative Form

x_{1} = 0, x_{2} \approx 1.118689, x_{3} = 35

Show Solution