Solve p(200-p)-[40025(200-p)]

Question

Simplify the expression

40225 p - p^{2} - 8005000

Evaluate

p (200 - p) - (40025 (200 - p))

Multiply the terms

p (200 - p) - 40025 (200 - p)

Expand the expression

More Steps

Calculate

p (200 - p)

Apply the distributive property

p \times 200 - p \times p

Use the commutative property to reorder the terms

200 p - p \times p

Multiply the terms

200 p - p^{2}

200 p - p^{2} - 40025 (200 - p)

Expand the expression

More Steps

Calculate

- 40025 (200 - p)

Apply the distributive property

- 40025 \times 200 - (- 40025 p)

Multiply the numbers

- 8005000 - (- 40025 p)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

- 8005000 + 40025 p

200 p - p^{2} - 8005000 + 40025 p

Solution

More Steps

Evaluate

200 p + 40025 p

Collect like terms by calculating the sum or difference of their coefficients

(200 + 40025) p

Add the numbers

40225 p

40225 p - p^{2} - 8005000

Show Solution

Factor the expression

(p - 40025) (200 - p)

Evaluate

p (200 - p) - (40025 (200 - p))

Multiply the terms

p (200 - p) - 40025 (200 - p)

Solution

(p - 40025) (200 - p)

Show Solution

Find the roots

p_{1} = 200, p_{2} = 40025

Evaluate

p (200 - p) - (40025 (200 - p))

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

p (200 - p) - (40025 (200 - p)) = 0

Multiply the terms

p (200 - p) - 40025 (200 - p) = 0

Calculate

More Steps

Evaluate

p (200 - p) - 40025 (200 - p)

Expand the expression

More Steps

Calculate

p (200 - p)

Apply the distributive property

p \times 200 - p \times p

Use the commutative property to reorder the terms

200 p - p \times p

Multiply the terms

200 p - p^{2}

200 p - p^{2} - 40025 (200 - p)

Expand the expression

More Steps

Calculate

- 40025 (200 - p)

Apply the distributive property

- 40025 \times 200 - (- 40025 p)

Multiply the numbers

- 8005000 - (- 40025 p)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

- 8005000 + 40025 p

200 p - p^{2} - 8005000 + 40025 p

Add the terms

More Steps

Evaluate

200 p + 40025 p

Collect like terms by calculating the sum or difference of their coefficients

(200 + 40025) p

Add the numbers

40225 p

40225 p - p^{2} - 8005000

40225 p - p^{2} - 8005000 = 0

Factor the expression

More Steps

Evaluate

40225 p - p^{2} - 8005000

Reorder the terms

- p^{2} + 40225 p - 8005000

Rewrite the expression

- p^{2} + (200 + 40025) p - 8005000

Calculate

- p^{2} + 200 p + 40025 p - 8005000

Rewrite the expression

- p \times p + p \times 200 + 40025 p - 40025 \times 200

Factor out - p from the expression

- p (p - 200) + 40025 p - 40025 \times 200

Factor out 40025 from the expression

- p (p - 200) + 40025 (p - 200)

Factor out p - 200 from the expression

(- p + 40025) (p - 200)

(- p + 40025) (p - 200) = 0

When the product of factors equals 0,at least one factor is 0

- p + 40025 = 0 p - 200 = 0

Solve the equation for p

More Steps

Evaluate

- p + 40025 = 0

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

- p = 0 - 40025

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

- p = - 40025

Change the signs on both sides of the equation

p = 40025

p = 40025 p - 200 = 0

Solve the equation for p

More Steps

Evaluate

p - 200 = 0

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

p = 0 + 200

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

p = 200

p = 40025 p = 200

Solution

p_{1} = 200, p_{2} = 40025

Show Solution