Solve n n-1 n-2 n-3

Question

Simplify the expression

n^{2} - 3 n - 3

Evaluate

n \times n - 1 \times n - 2 n - 3

Multiply the terms

n^{2} - 1 \times n - 2 n - 3

Multiply the terms

n^{2} - n - 2 n - 3

Solution

More Steps

Evaluate

- n - 2 n

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

(- 1 - 2) n

Subtract the numbers

- 3 n

n^{2} - 3 n - 3

Show Solution

Find the roots

n_{1} = \frac{3 - 21}{2}, n_{2} = \frac{3 + 21}{2}

Alternative Form

n_{1} \approx - 0.791288, n_{2} \approx 3.791288

Evaluate

n \times n - 1 \times n - 2 n - 3

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

n \times n - 1 \times n - 2 n - 3 = 0

Multiply the terms

n^{2} - 1 \times n - 2 n - 3 = 0

Any expression multiplied by 1 remains the same

n^{2} - n - 2 n - 3 = 0

Subtract the terms

More Steps

Simplify

n^{2} - n - 2 n

Subtract the terms

More Steps

Evaluate

- n - 2 n

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

(- 1 - 2) n

Subtract the numbers

- 3 n

n^{2} - 3 n

n^{2} - 3 n - 3 = 0

Substitute a= 1,b= - 3 and c= - 3 into the quadratic formula n = \frac{- b \pm b ^{2} - 4 a c}{2 a}

n = \frac{3 \pm ( - 3 ) ^{2} - 4 ( - 3 )}{2}

Simplify the expression

More Steps

Evaluate

(- 3)^{2} - 4 (- 3)

Multiply the numbers

More Steps

Evaluate

4 (- 3)

Multiplying or dividing an odd number of negative terms equals a negative

- 4 \times 3

Multiply the numbers

- 12

(- 3)^{2} - (- 12)

Rewrite the expression

3^{2} - (- 12)

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

3^{2} + 12

Evaluate the power

9 + 12

Add the numbers

21

n = \frac{3 \pm 21}{2}

Separate the equation into 2 possible cases

n = \frac{3 + 21}{2} n = \frac{3 - 21}{2}

Solution

n_{1} = \frac{3 - 21}{2}, n_{2} = \frac{3 + 21}{2}

Alternative Form

n_{1} \approx - 0.791288, n_{2} \approx 3.791288

Show Solution