Solve n(n-2)=2400

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

n_{1} = - 48, n_{2} = 50

Evaluate

n (n - 2) = 2400

Expand the expression

More Steps

Evaluate

n (n - 2)

Apply the distributive property

n \times n - n \times 2

Multiply the terms

n^{2} - n \times 2

Use the commutative property to reorder the terms

n^{2} - 2 n

n^{2} - 2 n = 2400

Move the expression to the left side

n^{2} - 2 n - 2400 = 0

Factor the expression

More Steps

Evaluate

n^{2} - 2 n - 2400

Rewrite the expression

n^{2} + (48 - 50) n - 2400

Calculate

n^{2} + 48 n - 50 n - 2400

Rewrite the expression

n \times n + n \times 48 - 50 n - 50 \times 48

Factor out n from the expression

n (n + 48) - 50 n - 50 \times 48

Factor out - 50 from the expression

n (n + 48) - 50 (n + 48)

Factor out n + 48 from the expression

(n - 50) (n + 48)

(n - 50) (n + 48) = 0

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

n - 50 = 0 n + 48 = 0

Solve the equation for n

More Steps

Evaluate

n - 50 = 0

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

n = 0 + 50

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

n = 50

n = 50 n + 48 = 0

Solve the equation for n

More Steps

Evaluate

n + 48 = 0

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

n = 0 - 48

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

n = - 48

n = 50 n = - 48

Solution

n_{1} = - 48, n_{2} = 50

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