Solve 29/p^6784-20

Question

Simplify the expression

\frac{22736 - 20 p ^{6}}{p ^{6}}

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p = 0

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p_{1} = - \frac{6 17762500}{5}, p_{2} = \frac{6 17762500}{5}

Alternative Form

p_{1} \approx - 3.230581, p_{2} \approx 3.230581

Evaluate

\frac{29}{p ^{6}} \times 784 - 20

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

\frac{29}{p ^{6}} \times 784 - 20 = 0

The only way a power can not be 0 is when the base not equals 0

\frac{29}{p ^{6}} \times 784 - 20 = 0, p \neq = 0

Calculate

\frac{29}{p ^{6}} \times 784 - 20 = 0

Multiply the terms

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\frac{22736}{p ^{6}} - 20 = 0

Subtract the terms

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\frac{22736 - 20 p ^{6}}{p ^{6}} = 0

Cross multiply

22736 - 20 p^{6} = p^{6} \times 0

Simplify the equation

22736 - 20 p^{6} = 0

Rewrite the expression

- 20 p^{6} = - 22736

Change the signs on both sides of the equation

20 p^{6} = 22736

Divide both sides

\frac{20 p ^{6}}{20} = \frac{22736}{20}

Divide the numbers

p^{6} = \frac{22736}{20}

Cancel out the common factor 4

p^{6} = \frac{5684}{5}

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

p = \pm 6 \frac{5684}{5}

Simplify the expression

More Steps

p = \pm \frac{6 17762500}{5}

Separate the equation into 2 possible cases

p = \frac{6 17762500}{5} p = - \frac{6 17762500}{5}

Check if the solution is in the defined range

p = \frac{6 17762500}{5} p = - \frac{6 17762500}{5}, p \neq = 0

Find the intersection of the solution and the defined range

p = \frac{6 17762500}{5} p = - \frac{6 17762500}{5}

Solution

p_{1} = - \frac{6 17762500}{5}, p_{2} = \frac{6 17762500}{5}

Alternative Form

p_{1} \approx - 3.230581, p_{2} \approx 3.230581

Show Solution