Solve 8q^2-48q^64

Question

Simplify the expression

8 q^{2} - 192 q^{6}

Evaluate

8 q^{2} - 48 q^{6} \times 4

Solution

8 q^{2} - 192 q^{6}

Show Solution

8 q^{2} (1 - 24 q^{4})

Evaluate

8 q^{2} - 48 q^{6} \times 4

Multiply the terms

8 q^{2} - 192 q^{6}

Rewrite the expression

8 q^{2} - 8 q^{2} \times 24 q^{4}

Solution

8 q^{2} (1 - 24 q^{4})

Show Solution

q_{1} = - \frac{4 54}{6}, q_{2} = 0, q_{3} = \frac{4 54}{6}

Alternative Form

q_{1} \approx - 0.451801, q_{2} = 0, q_{3} \approx 0.451801

Evaluate

8 q^{2} - 48 q^{6} \times 4

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

8 q^{2} - 48 q^{6} \times 4 = 0

Multiply the terms

8 q^{2} - 192 q^{6} = 0

Factor the expression

8 q^{2} (1 - 24 q^{4}) = 0

Divide both sides

q^{2} (1 - 24 q^{4}) = 0

Separate the equation into 2 possible cases

q^{2} = 0 1 - 24 q^{4} = 0

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

q = 0 1 - 24 q^{4} = 0

Solve the equation

More Steps

Evaluate

1 - 24 q^{4} = 0

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

- 24 q^{4} = 0 - 1

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

- 24 q^{4} = - 1

Change the signs on both sides of the equation

24 q^{4} = 1

Divide both sides

\frac{24 q ^{4}}{24} = \frac{1}{24}

Divide the numbers

q^{4} = \frac{1}{24}

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

q = \pm 4 \frac{1}{24}

Simplify the expression

More Steps

Evaluate

4 \frac{1}{24}

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

\frac{4 1}{4 24}

Simplify the radical expression

\frac{1}{4 24}

Multiply by the Conjugate

\frac{4 2 4 ^{3}}{4 24 \times 4 2 4 ^{3}}

Simplify

\frac{4 4 54}{4 24 \times 4 2 4 ^{3}}

Multiply the numbers

\frac{4 4 54}{24}

Cancel out the common factor 4

\frac{4 54}{6}

q = \pm \frac{4 54}{6}

Separate the equation into 2 possible cases

q = \frac{4 54}{6} q = - \frac{4 54}{6}

q = 0 q = \frac{4 54}{6} q = - \frac{4 54}{6}

Solution

q_{1} = - \frac{4 54}{6}, q_{2} = 0, q_{3} = \frac{4 54}{6}

Alternative Form

q_{1} \approx - 0.451801, q_{2} = 0, q_{3} \approx 0.451801

Show Solution