Solve (2x^2 - 6x - 4)(4x^2 2x - 7)

Question

Simplify the expression

16 x^{5} - 14 x^{2} - 48 x^{4} + 42 x - 32 x^{3} + 28

Evaluate

(2 x^{2} - 6 x - 4) (4 x^{2} \times 2 x - 7)

Multiply

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Evaluate

4 x^{2} \times 2 x

Multiply the terms

8 x^{2} \times x

Multiply the terms with the same base by adding their exponents

8 x^{2 + 1}

Add the numbers

8 x^{3}

(2 x^{2} - 6 x - 4) (8 x^{3} - 7)

Apply the distributive property

2 x^{2} \times 8 x^{3} - 2 x^{2} \times 7 - 6 x \times 8 x^{3} - (- 6 x \times 7) - 4 \times 8 x^{3} - (- 4 \times 7)

Multiply the terms

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Evaluate

2 x^{2} \times 8 x^{3}

Multiply the numbers

16 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}

16 x^{5}

16 x^{5} - 2 x^{2} \times 7 - 6 x \times 8 x^{3} - (- 6 x \times 7) - 4 \times 8 x^{3} - (- 4 \times 7)

Multiply the numbers

16 x^{5} - 14 x^{2} - 6 x \times 8 x^{3} - (- 6 x \times 7) - 4 \times 8 x^{3} - (- 4 \times 7)

Multiply the terms

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Evaluate

- 6 x \times 8 x^{3}

Multiply the numbers

- 48 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}

- 48 x^{4}

16 x^{5} - 14 x^{2} - 48 x^{4} - (- 6 x \times 7) - 4 \times 8 x^{3} - (- 4 \times 7)

Multiply the numbers

16 x^{5} - 14 x^{2} - 48 x^{4} - (- 42 x) - 4 \times 8 x^{3} - (- 4 \times 7)

Multiply the numbers

16 x^{5} - 14 x^{2} - 48 x^{4} - (- 42 x) - 32 x^{3} - (- 4 \times 7)

Multiply the numbers

16 x^{5} - 14 x^{2} - 48 x^{4} - (- 42 x) - 32 x^{3} - (- 28)

Solution

16 x^{5} - 14 x^{2} - 48 x^{4} + 42 x - 32 x^{3} + 28

Show Solution

Factor the expression

2 (x^{2} - 3 x - 2) (8 x^{3} - 7)

Evaluate

(2 x^{2} - 6 x - 4) (4 x^{2} \times 2 x - 7)

Multiply

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Evaluate

4 x^{2} \times 2 x

Multiply the terms

8 x^{2} \times x

Multiply the terms with the same base by adding their exponents

8 x^{2 + 1}

Add the numbers

8 x^{3}

(2 x^{2} - 6 x - 4) (8 x^{3} - 7)

Solution

2 (x^{2} - 3 x - 2) (8 x^{3} - 7)

Show Solution

Find the roots

x_{1} = \frac{3 - 17}{2}, x_{2} = \frac{3 7}{2}, x_{3} = \frac{3 + 17}{2}

Alternative Form

x_{1} \approx - 0.561553, x_{2} \approx 0.956466, x_{3} \approx 3.561553

Evaluate

(2 x^{2} - 6 x - 4) (4 x^{2} \times 2 x - 7)

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

(2 x^{2} - 6 x - 4) (4 x^{2} \times 2 x - 7) = 0

Multiply

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Multiply the terms

4 x^{2} \times 2 x

Multiply the terms

8 x^{2} \times x

Multiply the terms with the same base by adding their exponents

8 x^{2 + 1}

Add the numbers

8 x^{3}

(2 x^{2} - 6 x - 4) (8 x^{3} - 7) = 0

Separate the equation into 2 possible cases

2 x^{2} - 6 x - 4 = 0 8 x^{3} - 7 = 0

Solve the equation

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Evaluate

2 x^{2} - 6 x - 4 = 0

Substitute a= 2,b= - 6 and c= - 4 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{6 \pm ( - 6 ) ^{2} - 4 \times 2 ( - 4 )}{2 \times 2}

Simplify the expression

x = \frac{6 \pm ( - 6 ) ^{2} - 4 \times 2 ( - 4 )}{4}

Simplify the expression

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Evaluate

(- 6)^{2} - 4 \times 2 (- 4)

Multiply

(- 6)^{2} - (- 32)

Rewrite the expression

6^{2} - (- 32)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

6^{2} + 32

Evaluate the power

36 + 32

Add the numbers

68

x = \frac{6 \pm 68}{4}

Simplify the radical expression

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Evaluate

68

Write the expression as a product where the root of one of the factors can be evaluated

4 \times 17

Write the number in exponential form with the base of 2

2^{2} \times 17

The root of a product is equal to the product of the roots of each factor

2^{2} \times 17

Reduce the index of the radical and exponent with 2

217

x = \frac{6 \pm 2 17}{4}

Separate the equation into 2 possible cases

x = \frac{6 + 2 17}{4} x = \frac{6 - 2 17}{4}

Simplify the expression

x = \frac{3 + 17}{2} x = \frac{6 - 2 17}{4}

Simplify the expression

x = \frac{3 + 17}{2} x = \frac{3 - 17}{2}

x = \frac{3 + 17}{2} x = \frac{3 - 17}{2} 8 x^{3} - 7 = 0

Solve the equation

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Evaluate

8 x^{3} - 7 = 0

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

8 x^{3} = 0 + 7

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

8 x^{3} = 7

Divide both sides

\frac{8 x ^{3}}{8} = \frac{7}{8}

Divide the numbers

x^{3} = \frac{7}{8}

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

3 x^{3} = 3 \frac{7}{8}

Calculate

x = 3 \frac{7}{8}

Simplify the root

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Evaluate

3 \frac{7}{8}

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

\frac{3 7}{3 8}

Simplify the radical expression

\frac{3 7}{2}

x = \frac{3 7}{2}

x = \frac{3 + 17}{2} x = \frac{3 - 17}{2} x = \frac{3 7}{2}

Solution

x_{1} = \frac{3 - 17}{2}, x_{2} = \frac{3 7}{2}, x_{3} = \frac{3 + 17}{2}

Alternative Form

x_{1} \approx - 0.561553, x_{2} \approx 0.956466, x_{3} \approx 3.561553

Show Solution