Solve w^2-16w^48 - ScanMath

Question

Simplify the expression

w^{2} - 128 w^{4}

Evaluate

w^{2} - 16 w^{4} \times 8

Solution

w^{2} - 128 w^{4}

Show Solution

w^{2} (1 - 128 w^{2})

Evaluate

w^{2} - 16 w^{4} \times 8

Multiply the terms

w^{2} - 128 w^{4}

Rewrite the expression

w^{2} - w^{2} \times 128 w^{2}

Solution

w^{2} (1 - 128 w^{2})

Show Solution

w_{1} = - \frac{2}{16}, w_{2} = 0, w_{3} = \frac{2}{16}

Alternative Form

w_{1} \approx - 0.088388, w_{2} = 0, w_{3} \approx 0.088388

Evaluate

w^{2} - 16 w^{4} \times 8

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

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

Multiply the terms

w^{2} - 128 w^{4} = 0

Factor the expression

w^{2} (1 - 128 w^{2}) = 0

Separate the equation into 2 possible cases

w^{2} = 0 1 - 128 w^{2} = 0

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

w = 0 1 - 128 w^{2} = 0

Solve the equation

More Steps

Evaluate

1 - 128 w^{2} = 0

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

- 128 w^{2} = 0 - 1

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

- 128 w^{2} = - 1

Change the signs on both sides of the equation

128 w^{2} = 1

Divide both sides

\frac{128 w ^{2}}{128} = \frac{1}{128}

Divide the numbers

w^{2} = \frac{1}{128}

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

w = \pm \frac{1}{128}

Simplify the expression

More Steps

Evaluate

\frac{1}{128}

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

\frac{1}{128}

Simplify the radical expression

\frac{1}{128}

Simplify the radical expression

\frac{1}{8 2}

Multiply by the Conjugate

\frac{2}{8 2 \times 2}

Multiply the numbers

\frac{2}{16}

w = \pm \frac{2}{16}

Separate the equation into 2 possible cases

w = \frac{2}{16} w = - \frac{2}{16}

w = 0 w = \frac{2}{16} w = - \frac{2}{16}

Solution

w_{1} = - \frac{2}{16}, w_{2} = 0, w_{3} = \frac{2}{16}

Alternative Form

w_{1} \approx - 0.088388, w_{2} = 0, w_{3} \approx 0.088388

Show Solution