Solve 1089 = n/2(5n-11)

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

n_{1} = - \frac{99}{5}, n_{2} = 22

Alternative Form

n_{1} = - 19.8, n_{2} = 22

Evaluate

1089 = \frac{n}{2} (5 n - 11)

Multiply the terms

1089 = \frac{n ( 5 n - 11 )}{2}

Swap the sides

\frac{n ( 5 n - 11 )}{2} = 1089

Multiply both sides of the equation by LCD

\frac{n ( 5 n - 11 )}{2} \times 2 = 1089 \times 2

Simplify the equation

More Steps

Evaluate

\frac{n ( 5 n - 11 )}{2} \times 2

Simplify

n (5 n - 11)

Apply the distributive property

n \times 5 n - n \times 11

Multiply the terms

More Steps

Evaluate

n \times 5 n

Use the commutative property to reorder the terms

5 n \times n

Multiply the terms

5 n^{2}

5 n^{2} - n \times 11

Use the commutative property to reorder the terms

5 n^{2} - 11 n

5 n^{2} - 11 n = 1089 \times 2

Simplify the equation

5 n^{2} - 11 n = 2178

Move the expression to the left side

5 n^{2} - 11 n - 2178 = 0

Factor the expression

More Steps

Evaluate

5 n^{2} - 11 n - 2178

Rewrite the expression

5 n^{2} + (99 - 110) n - 2178

Calculate

5 n^{2} + 99 n - 110 n - 2178

Rewrite the expression

n \times 5 n + n \times 99 - 22 \times 5 n - 22 \times 99

Factor out n from the expression

n (5 n + 99) - 22 \times 5 n - 22 \times 99

Factor out - 22 from the expression

n (5 n + 99) - 22 (5 n + 99)

Factor out 5 n + 99 from the expression

(n - 22) (5 n + 99)

(n - 22) (5 n + 99) = 0

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

n - 22 = 0 5 n + 99 = 0

Solve the equation for n

More Steps

Evaluate

n - 22 = 0

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

n = 0 + 22

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

n = 22

n = 22 5 n + 99 = 0

Solve the equation for n

More Steps

Evaluate

5 n + 99 = 0

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

5 n = 0 - 99

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

5 n = - 99

Divide both sides

\frac{5 n}{5} = \frac{- 99}{5}

Divide the numbers

n = \frac{- 99}{5}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

n = - \frac{99}{5}

n = 22 n = - \frac{99}{5}

Solution

n_{1} = - \frac{99}{5}, n_{2} = 22

Alternative Form

n_{1} = - 19.8, n_{2} = 22

Show Solution