Solve (2x^2-4)(2x-1-3/2x)

Question

(2 x^{2} - 4) (2 x - 1 - \frac{3}{2} x)

Simplify the expression

x^{3} - 2 x^{2} - 2 x + 4

Evaluate

(2 x^{2} - 4) (2 x - 1 - \frac{3}{2} x)

Subtract the terms

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Evaluate

2 x - \frac{3}{2} x

Collect like terms by calculating the sum or difference of their coefficients

(2 - \frac{3}{2}) x

Subtract the numbers

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Evaluate

2 - \frac{3}{2}

Reduce fractions to a common denominator

\frac{2 \times 2}{2} - \frac{3}{2}

Write all numerators above the common denominator

\frac{2 \times 2 - 3}{2}

Multiply the numbers

\frac{4 - 3}{2}

Subtract the numbers

\frac{1}{2}

\frac{1}{2} x

(2 x^{2} - 4) (\frac{1}{2} x - 1)

Apply the distributive property

2 x^{2} \times \frac{1}{2} x - 2 x^{2} \times 1 - 4 \times \frac{1}{2} x - (- 4 \times 1)

Multiply the terms

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Evaluate

2 x^{2} \times \frac{1}{2} x

Multiply the numbers

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Evaluate

2 \times \frac{1}{2}

Reduce the numbers

1 \times 1

Simplify

1

x^{2} \times x

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

x^{2 + 1}

Add the numbers

x^{3}

x^{3} - 2 x^{2} \times 1 - 4 \times \frac{1}{2} x - (- 4 \times 1)

Any expression multiplied by 1 remains the same

x^{3} - 2 x^{2} - 4 \times \frac{1}{2} x - (- 4 \times 1)

Multiply the numbers

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Evaluate

- 4 \times \frac{1}{2}

Reduce the numbers

- 2 \times 1

Simplify

- 2

x^{3} - 2 x^{2} - 2 x - (- 4 \times 1)

Any expression multiplied by 1 remains the same

x^{3} - 2 x^{2} - 2 x - (- 4)

Solution

x^{3} - 2 x^{2} - 2 x + 4

Show Solution

Factor the expression

(x^{2} - 2) (x - 2)

Evaluate

(2 x^{2} - 4) (2 x - 1 - \frac{3}{2} x)

Subtract the terms

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Evaluate

2 x - \frac{3}{2} x

Collect like terms by calculating the sum or difference of their coefficients

(2 - \frac{3}{2}) x

Subtract the numbers

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Evaluate

2 - \frac{3}{2}

Reduce fractions to a common denominator

\frac{2 \times 2}{2} - \frac{3}{2}

Write all numerators above the common denominator

\frac{2 \times 2 - 3}{2}

Multiply the numbers

\frac{4 - 3}{2}

Subtract the numbers

\frac{1}{2}

\frac{1}{2} x

(2 x^{2} - 4) (\frac{1}{2} x - 1)

Factor the expression

2 (x^{2} - 2) (\frac{1}{2} x - 1)

Factor the expression

2 (x^{2} - 2) \times \frac{1}{2} (x - 2)

Solution

(x^{2} - 2) (x - 2)

Show Solution

Find the roots

x_{1} = - 2, x_{2} = 2, x_{3} = 2

Alternative Form

x_{1} \approx - 1.414214, x_{2} \approx 1.414214, x_{3} = 2

Evaluate

(2 x^{2} - 4) (2 x - 1 - \frac{3}{2} x)

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

(2 x^{2} - 4) (2 x - 1 - \frac{3}{2} x) = 0

Subtract the terms

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Simplify

2 x - 1 - \frac{3}{2} x

Subtract the terms

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Evaluate

2 x - \frac{3}{2} x

Collect like terms by calculating the sum or difference of their coefficients

(2 - \frac{3}{2}) x

Subtract the numbers

\frac{1}{2} x

\frac{1}{2} x - 1

(2 x^{2} - 4) (\frac{1}{2} x - 1) = 0

Separate the equation into 2 possible cases

2 x^{2} - 4 = 0 \frac{1}{2} x - 1 = 0

Solve the equation

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Evaluate

2 x^{2} - 4 = 0

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

2 x^{2} = 0 + 4

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

2 x^{2} = 4

Divide both sides

\frac{2 x ^{2}}{2} = \frac{4}{2}

Divide the numbers

x^{2} = \frac{4}{2}

Divide the numbers

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Evaluate

\frac{4}{2}

Reduce the numbers

\frac{2}{1}

Calculate

2

x^{2} = 2

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

x = \pm 2

Separate the equation into 2 possible cases

x = 2 x = - 2

x = 2 x = - 2 \frac{1}{2} x - 1 = 0

Solve the equation

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Evaluate

\frac{1}{2} x - 1 = 0

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

\frac{1}{2} x = 0 + 1

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

\frac{1}{2} x = 1

Multiply by the reciprocal

\frac{1}{2} x \times 2 = 1 \times 2

Multiply

x = 1 \times 2

Any expression multiplied by 1 remains the same

x = 2

x = 2 x = - 2 x = 2

Solution

x_{1} = - 2, x_{2} = 2, x_{3} = 2

Alternative Form

x_{1} \approx - 1.414214, x_{2} \approx 1.414214, x_{3} = 2

Show Solution