Solve 2(x^2) 3x=2(x 1) 1

Question

Solve the equation

x_{1} = - \frac{3}{3}, x_{2} = 0, x_{3} = \frac{3}{3}

Alternative Form

x_{1} \approx - 0.57735, x_{2} = 0, x_{3} \approx 0.57735

Evaluate

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

Remove the parentheses

2 x^{2} \times 3 x = 2 x \times 1 \times 1

Simplify

x^{2} \times 3 x = x \times 1 \times 1

Multiply

More Steps

Evaluate

x^{2} \times 3 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 3

Add the numbers

x^{3} \times 3

Use the commutative property to reorder the terms

3 x^{3}

3 x^{3} = x \times 1 \times 1

Multiply the terms

3 x^{3} = x

Add or subtract both sides

3 x^{3} - x = 0

Factor the expression

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

Separate the equation into 2 possible cases

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

Solve the equation

More Steps

Evaluate

3 x^{2} - 1 = 0

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

3 x^{2} = 0 + 1

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

3 x^{2} = 1

Divide both sides

\frac{3 x ^{2}}{3} = \frac{1}{3}

Divide the numbers

x^{2} = \frac{1}{3}

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

x = \pm \frac{1}{3}

Simplify the expression

More Steps

Evaluate

\frac{1}{3}

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

\frac{1}{3}

Simplify the radical expression

\frac{1}{3}

Multiply by the Conjugate

\frac{3}{3 \times 3}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{3}{3}

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

Separate the equation into 2 possible cases

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

x = 0 x = \frac{3}{3} x = - \frac{3}{3}

Solution

x_{1} = - \frac{3}{3}, x_{2} = 0, x_{3} = \frac{3}{3}

Alternative Form

x_{1} \approx - 0.57735, x_{2} = 0, x_{3} \approx 0.57735

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