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

Question

Simplify the expression

- 3 x^{4} + 6 x^{3} + 6 x^{2}

Evaluate

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

Subtract the terms

More Steps

Simplify

x^{2} - 4 x^{2}

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

(1 - 4) x^{2}

Subtract the numbers

- 3 x^{2}

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

Remove the parentheses

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

Apply the distributive property

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

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

Multiply the terms

More Steps

Evaluate

- 3 x^{2} \times 2 x

Multiply the numbers

- 6 x^{2} \times x

Multiply the terms

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Evaluate

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}

- 6 x^{3}

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

Multiply the numbers

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

Solution

- 3 x^{4} + 6 x^{3} + 6 x^{2}

Show Solution

Find the roots

x_{1} = 1 - 3, x_{2} = 0, x_{3} = 1 + 3

Alternative Form

x_{1} \approx - 0.732051, x_{2} = 0, x_{3} \approx 2.732051

Evaluate

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

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

(x^{2} - 4 x^{2}) (x^{2} - 2 x - 2) = 0

Subtract the terms

More Steps

Simplify

x^{2} - 4 x^{2}

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

(1 - 4) x^{2}

Subtract the numbers

- 3 x^{2}

(- 3 x^{2}) (x^{2} - 2 x - 2) = 0

Remove the parentheses

- 3 x^{2} (x^{2} - 2 x - 2) = 0

Change the sign

3 x^{2} (x^{2} - 2 x - 2) = 0

Elimination the left coefficient

x^{2} (x^{2} - 2 x - 2) = 0

Separate the equation into 2 possible cases

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

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

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

Solve the equation

More Steps

Evaluate

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

Substitute a= 1,b= - 2 and c= - 2 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

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

Simplify the expression

More Steps

Evaluate

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

Multiply the numbers

(- 2)^{2} - (- 8)

Rewrite the expression

2^{2} - (- 8)

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

2^{2} + 8

Evaluate the power

4 + 8

Add the numbers

12

x = \frac{2 \pm 12}{2}

Simplify the radical expression

More Steps

Evaluate

12

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

4 \times 3

Write the number in exponential form with the base of 2

2^{2} \times 3

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

2^{2} \times 3

Reduce the index of the radical and exponent with 2

23

x = \frac{2 \pm 2 3}{2}

Separate the equation into 2 possible cases

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

Simplify the expression

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

Simplify the expression

x = 1 + 3 x = 1 - 3

x = 0 x = 1 + 3 x = 1 - 3

Solution

x_{1} = 1 - 3, x_{2} = 0, x_{3} = 1 + 3

Alternative Form

x_{1} \approx - 0.732051, x_{2} = 0, x_{3} \approx 2.732051

Show Solution