Solve p^24-100382

Question

Simplify the expression

4 p^{2} - 100382

Evaluate

p^{2} \times 4 - 100382

Solution

4 p^{2} - 100382

Show Solution

2 (2 p^{2} - 50191)

Evaluate

p^{2} \times 4 - 100382

Use the commutative property to reorder the terms

4 p^{2} - 100382

Solution

2 (2 p^{2} - 50191)

Show Solution

p_{1} = - \frac{100382}{2}, p_{2} = \frac{100382}{2}

Alternative Form

p_{1} \approx - 158.415593, p_{2} \approx 158.415593

Evaluate

p^{2} \times 4 - 100382

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

p^{2} \times 4 - 100382 = 0

Use the commutative property to reorder the terms

4 p^{2} - 100382 = 0

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

4 p^{2} = 0 + 100382

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

4 p^{2} = 100382

Divide both sides

\frac{4 p ^{2}}{4} = \frac{100382}{4}

Divide the numbers

p^{2} = \frac{100382}{4}

Cancel out the common factor 2

p^{2} = \frac{50191}{2}

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

p = \pm \frac{50191}{2}

Simplify the expression

More Steps

Evaluate

\frac{50191}{2}

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

\frac{50191}{2}

Multiply by the Conjugate

\frac{50191 \times 2}{2 \times 2}

Multiply the numbers

More Steps

Evaluate

50191 \times 2

The product of roots with the same index is equal to the root of the product

50191 \times 2

Calculate the product

100382

\frac{100382}{2 \times 2}

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

\frac{100382}{2}

p = \pm \frac{100382}{2}

Separate the equation into 2 possible cases

p = \frac{100382}{2} p = - \frac{100382}{2}

Solution

p_{1} = - \frac{100382}{2}, p_{2} = \frac{100382}{2}

Alternative Form

p_{1} \approx - 158.415593, p_{2} \approx 158.415593

Show Solution