Solve 20p^2-2019 - ScanMath

Question

Find the roots

p_{1} = - \frac{10095}{10}, p_{2} = \frac{10095}{10}

Alternative Form

p_{1} \approx - 10.047388, p_{2} \approx 10.047388

Evaluate

20 p^{2} - 2019

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

20 p^{2} - 2019 = 0

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

20 p^{2} = 0 + 2019

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

20 p^{2} = 2019

Divide both sides

\frac{20 p ^{2}}{20} = \frac{2019}{20}

Divide the numbers

p^{2} = \frac{2019}{20}

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

p = \pm \frac{2019}{20}

Simplify the expression

More Steps

Evaluate

\frac{2019}{20}

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

\frac{2019}{20}

Simplify the radical expression

More Steps

Evaluate

20

Write the expression as a product where the root of one of the factors can be evaluated

4 \times 5

Write the number in exponential form with the base of 2

2^{2} \times 5

The root of a product is equal to the product of the roots of each factor

2^{2} \times 5

Reduce the index of the radical and exponent with 2

25

\frac{2019}{2 5}

Multiply by the Conjugate

\frac{2019 \times 5}{2 5 \times 5}

Multiply the numbers

More Steps

Evaluate

2019 \times 5

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

2019 \times 5

Calculate the product

10095

\frac{10095}{2 5 \times 5}

Multiply the numbers

More Steps

Evaluate

25 \times 5

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

2 \times 5

Multiply the terms

10

\frac{10095}{10}

p = \pm \frac{10095}{10}

Separate the equation into 2 possible cases

p = \frac{10095}{10} p = - \frac{10095}{10}

Solution

p_{1} = - \frac{10095}{10}, p_{2} = \frac{10095}{10}

Alternative Form

p_{1} \approx - 10.047388, p_{2} \approx 10.047388

Show Solution