Solve x^34x^2 =9x^36

Question

Solve the equation

x_{1} = - \frac{3 6}{2}, x_{2} = 0, x_{3} = \frac{3 6}{2}

Alternative Form

x_{1} \approx - 3.674235, x_{2} = 0, x_{3} \approx 3.674235

Evaluate

x^{3} \times 4 x^{2} = 9 x^{3} \times 6

Multiply

More Steps

Evaluate

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

Multiply the terms with the same base by adding their exponents

x^{3 + 2} \times 4

Add the numbers

x^{5} \times 4

Use the commutative property to reorder the terms

4 x^{5}

4 x^{5} = 9 x^{3} \times 6

Multiply the terms

4 x^{5} = 54 x^{3}

Add or subtract both sides

4 x^{5} - 54 x^{3} = 0

Factor the expression

2 x^{3} (2 x^{2} - 27) = 0

Divide both sides

x^{3} (2 x^{2} - 27) = 0

Separate the equation into 2 possible cases

x^{3} = 0 2 x^{2} - 27 = 0

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

x = 0 2 x^{2} - 27 = 0

Solve the equation

More Steps

Evaluate

2 x^{2} - 27 = 0

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

2 x^{2} = 0 + 27

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

2 x^{2} = 27

Divide both sides

\frac{2 x ^{2}}{2} = \frac{27}{2}

Divide the numbers

x^{2} = \frac{27}{2}

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

x = \pm \frac{27}{2}

Simplify the expression

More Steps

Evaluate

\frac{27}{2}

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

\frac{27}{2}

Simplify the radical expression

\frac{3 3}{2}

Multiply by the Conjugate

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

Multiply the numbers

\frac{3 6}{2 \times 2}

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

\frac{3 6}{2}

x = \pm \frac{3 6}{2}

Separate the equation into 2 possible cases

x = \frac{3 6}{2} x = - \frac{3 6}{2}

x = 0 x = \frac{3 6}{2} x = - \frac{3 6}{2}

Solution

x_{1} = - \frac{3 6}{2}, x_{2} = 0, x_{3} = \frac{3 6}{2}

Alternative Form

x_{1} \approx - 3.674235, x_{2} = 0, x_{3} \approx 3.674235

Show Solution