Solve k^2 - 3k - 54

Question

Factor the expression

(k - 9) (k + 6)

Evaluate

k^{2} - 3 k - 54

Rewrite the expression

k^{2} + (6 - 9) k - 54

Calculate

k^{2} + 6 k - 9 k - 54

Rewrite the expression

k \times k + k \times 6 - 9 k - 9 \times 6

Factor out k from the expression

k (k + 6) - 9 k - 9 \times 6

Factor out - 9 from the expression

k (k + 6) - 9 (k + 6)

Solution

(k - 9) (k + 6)

Show Solution

k_{1} = - 6, k_{2} = 9

Evaluate

k^{2} - 3 k - 54

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

k^{2} - 3 k - 54 = 0

Factor the expression

More Steps

Evaluate

k^{2} - 3 k - 54

Rewrite the expression

k^{2} + (6 - 9) k - 54

Calculate

k^{2} + 6 k - 9 k - 54

Rewrite the expression

k \times k + k \times 6 - 9 k - 9 \times 6

Factor out k from the expression

k (k + 6) - 9 k - 9 \times 6

Factor out - 9 from the expression

k (k + 6) - 9 (k + 6)

Factor out k + 6 from the expression

(k - 9) (k + 6)

(k - 9) (k + 6) = 0

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

k - 9 = 0 k + 6 = 0

Solve the equation for k

More Steps

Evaluate

k - 9 = 0

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

k = 0 + 9

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

k = 9

k = 9 k + 6 = 0

Solve the equation for k

More Steps

Evaluate

k + 6 = 0

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

k = 0 - 6

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

k = - 6

k = 9 k = - 6

Solution

k_{1} = - 6, k_{2} = 9

Show Solution