Solve w^3/52=w^5/2

Question

Solve the equation

w_{1} = - \frac{26}{26}, w_{2} = 0, w_{3} = \frac{26}{26}

Alternative Form

w_{1} \approx - 0.196116, w_{2} = 0, w_{3} \approx 0.196116

Evaluate

\frac{w ^{3}}{52} = \frac{w ^{5}}{2}

Cross multiply

w^{3} \times 2 = 52 w^{5}

Simplify the equation

2 w^{3} = 52 w^{5}

Rewrite the expression

2 w^{3} = 2 \times 26 w^{5}

Evaluate

w^{3} = 26 w^{5}

Move the expression to the left side

w^{3} - 26 w^{5} = 0

Factor the expression

w^{3} (1 - 26 w^{2}) = 0

Separate the equation into 2 possible cases

w^{3} = 0 1 - 26 w^{2} = 0

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

w = 0 1 - 26 w^{2} = 0

Solve the equation

More Steps

Evaluate

1 - 26 w^{2} = 0

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

- 26 w^{2} = 0 - 1

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

- 26 w^{2} = - 1

Change the signs on both sides of the equation

26 w^{2} = 1

Divide both sides

\frac{26 w ^{2}}{26} = \frac{1}{26}

Divide the numbers

w^{2} = \frac{1}{26}

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

w = \pm \frac{1}{26}

Simplify the expression

More Steps

Evaluate

\frac{1}{26}

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

\frac{1}{26}

Simplify the radical expression

\frac{1}{26}

Multiply by the Conjugate

\frac{26}{26 \times 26}

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

\frac{26}{26}

w = \pm \frac{26}{26}

Separate the equation into 2 possible cases

w = \frac{26}{26} w = - \frac{26}{26}

w = 0 w = \frac{26}{26} w = - \frac{26}{26}

Solution

w_{1} = - \frac{26}{26}, w_{2} = 0, w_{3} = \frac{26}{26}

Alternative Form

w_{1} \approx - 0.196116, w_{2} = 0, w_{3} \approx 0.196116

Show Solution