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

Question

Simplify the expression

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

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Factor the expression

(x - 1) (3 x^{2} + 4 + 2 x)

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Find the roots

x_{1} = - \frac{1}{3} - \frac{11}{3} i, x_{2} = - \frac{1}{3} + \frac{11}{3} i, x_{3} = 1

Alternative Form

x_{1} \approx - 0. \dot{3} - 1.105542 i, x_{2} \approx - 0. \dot{3} + 1.105542 i, x_{3} = 1

Evaluate

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

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

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

Multiply

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

Remove the parentheses

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

Multiply the terms

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

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

3 x^{3} - 4 - x^{2} + 2 x = 0

Factor the expression

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

Separate the equation into 2 possible cases

x - 1 = 0 3 x^{2} + 4 + 2 x = 0

Solve the equation

More Steps

x = 1 3 x^{2} + 4 + 2 x = 0

Solve the equation

More Steps

x = 1 x = - \frac{1}{3} + \frac{11}{3} i x = - \frac{1}{3} - \frac{11}{3} i

Solution

x_{1} = - \frac{1}{3} - \frac{11}{3} i, x_{2} = - \frac{1}{3} + \frac{11}{3} i, x_{3} = 1

Alternative Form

x_{1} \approx - 0. \dot{3} - 1.105542 i, x_{2} \approx - 0. \dot{3} + 1.105542 i, x_{3} = 1

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