Solve a^3 9a 1-6a^2 = 0

Question

Solve the equation

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

Alternative Form

a_{1} \approx - 0.816497, a_{2} = 0, a_{3} \approx 0.816497

Evaluate

a^{3} \times 9 a \times 1 - 6 a^{2} = 0

Multiply the terms

More Steps

Evaluate

a^{3} \times 9 a \times 1

Rewrite the expression

a^{3} \times 9 a

Multiply the terms with the same base by adding their exponents

a^{3 + 1} \times 9

Add the numbers

a^{4} \times 9

Use the commutative property to reorder the terms

9 a^{4}

9 a^{4} - 6 a^{2} = 0

Factor the expression

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

Divide both sides

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

Separate the equation into 2 possible cases

a^{2} = 0 3 a^{2} - 2 = 0

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

a = 0 3 a^{2} - 2 = 0

Solve the equation

More Steps

Evaluate

3 a^{2} - 2 = 0

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

3 a^{2} = 0 + 2

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

3 a^{2} = 2

Divide both sides

\frac{3 a ^{2}}{3} = \frac{2}{3}

Divide the numbers

a^{2} = \frac{2}{3}

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

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

Simplify the expression

More Steps

Evaluate

\frac{2}{3}

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

\frac{2}{3}

Multiply by the Conjugate

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

Multiply the numbers

\frac{6}{3 \times 3}

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

\frac{6}{3}

a = \pm \frac{6}{3}

Separate the equation into 2 possible cases

a = \frac{6}{3} a = - \frac{6}{3}

a = 0 a = \frac{6}{3} a = - \frac{6}{3}

Solution

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

Alternative Form

a_{1} \approx - 0.816497, a_{2} = 0, a_{3} \approx 0.816497

Show Solution