Solve p^2131-1-19

Question

Simplify the expression

131 p^{2} - 20

Evaluate

p^{2} \times 131 - 1 - 19

Use the commutative property to reorder the terms

131 p^{2} - 1 - 19

Solution

131 p^{2} - 20

Show Solution

p_{1} = - \frac{2 655}{131}, p_{2} = \frac{2 655}{131}

Alternative Form

p_{1} \approx - 0.390732, p_{2} \approx 0.390732

Evaluate

p^{2} \times 131 - 1 - 19

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

p^{2} \times 131 - 1 - 19 = 0

Use the commutative property to reorder the terms

131 p^{2} - 1 - 19 = 0

Subtract the numbers

131 p^{2} - 20 = 0

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

131 p^{2} = 0 + 20

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

131 p^{2} = 20

Divide both sides

\frac{131 p ^{2}}{131} = \frac{20}{131}

Divide the numbers

p^{2} = \frac{20}{131}

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

p = \pm \frac{20}{131}

Simplify the expression

More Steps

Evaluate

\frac{20}{131}

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

\frac{20}{131}

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{2 5}{131}

Multiply by the Conjugate

\frac{2 5 \times 131}{131 \times 131}

Multiply the numbers

More Steps

Evaluate

5 \times 131

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

5 \times 131

Calculate the product

655

\frac{2 655}{131 \times 131}

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

\frac{2 655}{131}

p = \pm \frac{2 655}{131}

Separate the equation into 2 possible cases

p = \frac{2 655}{131} p = - \frac{2 655}{131}

Solution

p_{1} = - \frac{2 655}{131}, p_{2} = \frac{2 655}{131}

Alternative Form

p_{1} \approx - 0.390732, p_{2} \approx 0.390732

Show Solution