Solve x^23x^2=4x^2

Question

Solve the equation

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

Alternative Form

x_{1} \approx - 1.154701, x_{2} = 0, x_{3} \approx 1.154701

Evaluate

x^{2} \times 3 x^{2} = 4 x^{2}

Multiply

More Steps

Evaluate

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

Multiply the terms with the same base by adding their exponents

x^{2 + 2} \times 3

Add the numbers

x^{4} \times 3

Use the commutative property to reorder the terms

3 x^{4}

3 x^{4} = 4 x^{2}

Add or subtract both sides

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

Factor the expression

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

Separate the equation into 2 possible cases

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

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

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

Solve the equation

More Steps

Evaluate

3 x^{2} - 4 = 0

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

3 x^{2} = 0 + 4

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

3 x^{2} = 4

Divide both sides

\frac{3 x ^{2}}{3} = \frac{4}{3}

Divide the numbers

x^{2} = \frac{4}{3}

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

x = \pm \frac{4}{3}

Simplify the expression

More Steps

Evaluate

\frac{4}{3}

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

\frac{4}{3}

Simplify the radical expression

\frac{2}{3}

Multiply by the Conjugate

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

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

\frac{2 3}{3}

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

Separate the equation into 2 possible cases

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

x = 0 x = \frac{2 3}{3} x = - \frac{2 3}{3}

Solution

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

Alternative Form

x_{1} \approx - 1.154701, x_{2} = 0, x_{3} \approx 1.154701

Show Solution