Solve 21q^2-27q^6

Question

Factor the expression

3 q^{2} (7 - 9 q^{4})

Evaluate

21 q^{2} - 27 q^{6}

Rewrite the expression

3 q^{2} \times 7 - 3 q^{2} \times 9 q^{4}

Solution

3 q^{2} (7 - 9 q^{4})

Show Solution

q_{1} = - \frac{4 63}{3}, q_{2} = 0, q_{3} = \frac{4 63}{3}

Alternative Form

q_{1} \approx - 0.939104, q_{2} = 0, q_{3} \approx 0.939104

Evaluate

21 q^{2} - 27 q^{6}

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

21 q^{2} - 27 q^{6} = 0

Factor the expression

3 q^{2} (7 - 9 q^{4}) = 0

Divide both sides

q^{2} (7 - 9 q^{4}) = 0

Separate the equation into 2 possible cases

q^{2} = 0 7 - 9 q^{4} = 0

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

q = 0 7 - 9 q^{4} = 0

Solve the equation

More Steps

Evaluate

7 - 9 q^{4} = 0

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

- 9 q^{4} = 0 - 7

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

- 9 q^{4} = - 7

Change the signs on both sides of the equation

9 q^{4} = 7

Divide both sides

\frac{9 q ^{4}}{9} = \frac{7}{9}

Divide the numbers

q^{4} = \frac{7}{9}

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

q = \pm 4 \frac{7}{9}

Simplify the expression

More Steps

Evaluate

4 \frac{7}{9}

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

\frac{4 7}{4 9}

Simplify the radical expression

\frac{4 7}{3}

Multiply by the Conjugate

\frac{4 7 \times 3}{3 \times 3}

Multiply the numbers

\frac{4 63}{3 \times 3}

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

\frac{4 63}{3}

q = \pm \frac{4 63}{3}

Separate the equation into 2 possible cases

q = \frac{4 63}{3} q = - \frac{4 63}{3}

q = 0 q = \frac{4 63}{3} q = - \frac{4 63}{3}

Solution

q_{1} = - \frac{4 63}{3}, q_{2} = 0, q_{3} = \frac{4 63}{3}

Alternative Form

q_{1} \approx - 0.939104, q_{2} = 0, q_{3} \approx 0.939104

Show Solution