Solve 16q^(4)-8q^(2) 1

Question

Simplify the expression

16 q^{4} - 8 q^{2}

Evaluate

16 q^{4} - 8 q^{2} \times 1

Solution

16 q^{4} - 8 q^{2}

Show Solution

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

Evaluate

16 q^{4} - 8 q^{2} \times 1

Multiply the terms

16 q^{4} - 8 q^{2}

Rewrite the expression

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

Solution

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

Show Solution

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

Alternative Form

q_{1} \approx - 0.707107, q_{2} = 0, q_{3} \approx 0.707107

Evaluate

16 q^{4} - 8 q^{2} \times 1

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

16 q^{4} - 8 q^{2} \times 1 = 0

Multiply the terms

16 q^{4} - 8 q^{2} = 0

Factor the expression

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

Divide both sides

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

Separate the equation into 2 possible cases

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

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

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

Solve the equation

More Steps

Evaluate

2 q^{2} - 1 = 0

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

2 q^{2} = 0 + 1

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

2 q^{2} = 1

Divide both sides

\frac{2 q ^{2}}{2} = \frac{1}{2}

Divide the numbers

q^{2} = \frac{1}{2}

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

q = \pm \frac{1}{2}

Simplify the expression

More Steps

Evaluate

\frac{1}{2}

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

\frac{1}{2}

Simplify the radical expression

\frac{1}{2}

Multiply by the Conjugate

\frac{2}{2 \times 2}

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

\frac{2}{2}

q = \pm \frac{2}{2}

Separate the equation into 2 possible cases

q = \frac{2}{2} q = - \frac{2}{2}

q = 0 q = \frac{2}{2} q = - \frac{2}{2}

Solution

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

Alternative Form

q_{1} \approx - 0.707107, q_{2} = 0, q_{3} \approx 0.707107

Show Solution