Solve ( n - 6 ) ( n - \frac { 1 } { 2 } )

Question

Simplify the expression

n^{2} - \frac{13}{2} n + 3

Evaluate

(n - 6) (n - \frac{1}{2})

Apply the distributive property

n \times n - n \times \frac{1}{2} - 6 n - (- 6 \times \frac{1}{2})

Multiply the terms

n^{2} - n \times \frac{1}{2} - 6 n - (- 6 \times \frac{1}{2})

Use the commutative property to reorder the terms

n^{2} - \frac{1}{2} n - 6 n - (- 6 \times \frac{1}{2})

Multiply the numbers

More Steps

Evaluate

- 6 \times \frac{1}{2}

Reduce the numbers

- 3 \times 1

Simplify

- 3

n^{2} - \frac{1}{2} n - 6 n - (- 3)

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

n^{2} - \frac{1}{2} n - 6 n + 3

Solution

More Steps

Evaluate

- \frac{1}{2} n - 6 n

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

(- \frac{1}{2} - 6) n

Subtract the numbers

More Steps

Evaluate

- \frac{1}{2} - 6

Reduce fractions to a common denominator

- \frac{1}{2} - \frac{6 \times 2}{2}

Write all numerators above the common denominator

\frac{- 1 - 6 \times 2}{2}

Multiply the numbers

\frac{- 1 - 12}{2}

Subtract the numbers

\frac{- 13}{2}

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

- \frac{13}{2}

- \frac{13}{2} n

n^{2} - \frac{13}{2} n + 3

Show Solution

Factor the expression

\frac{1}{2} (n - 6) (2 n - 1)

Evaluate

(n - 6) (n - \frac{1}{2})

Factor the expression

(n - 6) \times \frac{1}{2} (2 n - 1)

Solution

\frac{1}{2} (n - 6) (2 n - 1)

Show Solution

Find the roots

n_{1} = \frac{1}{2}, n_{2} = 6

Alternative Form

n_{1} = 0.5, n_{2} = 6

Evaluate

(n - 6) (n - \frac{1}{2})

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

(n - 6) (n - \frac{1}{2}) = 0

Separate the equation into 2 possible cases

n - 6 = 0 n - \frac{1}{2} = 0

Solve the equation

More Steps

Evaluate

n - 6 = 0

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

n = 0 + 6

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

n = 6

n = 6 n - \frac{1}{2} = 0

Solve the equation

More Steps

Evaluate

n - \frac{1}{2} = 0

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

n = 0 + \frac{1}{2}

Add the terms

n = \frac{1}{2}

n = 6 n = \frac{1}{2}

Solution

n_{1} = \frac{1}{2}, n_{2} = 6

Alternative Form

n_{1} = 0.5, n_{2} = 6

Show Solution