Solve 8k^2-10k-33

Question

Factor the expression

(2 k + 3) (4 k - 11)

Evaluate

8 k^{2} - 10 k - 33

Rewrite the expression

8 k^{2} + (- 22 + 12) k - 33

Calculate

8 k^{2} - 22 k + 12 k - 33

Rewrite the expression

2 k \times 4 k - 2 k \times 11 + 3 \times 4 k - 3 \times 11

Factor out 2 k from the expression

2 k (4 k - 11) + 3 \times 4 k - 3 \times 11

Factor out 3 from the expression

2 k (4 k - 11) + 3 (4 k - 11)

Solution

(2 k + 3) (4 k - 11)

Show Solution

k_{1} = - \frac{3}{2}, k_{2} = \frac{11}{4}

Alternative Form

k_{1} = - 1.5, k_{2} = 2.75

Evaluate

8 k^{2} - 10 k - 33

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

8 k^{2} - 10 k - 33 = 0

Factor the expression

More Steps

Evaluate

8 k^{2} - 10 k - 33

Rewrite the expression

8 k^{2} + (- 22 + 12) k - 33

Calculate

8 k^{2} - 22 k + 12 k - 33

Rewrite the expression

2 k \times 4 k - 2 k \times 11 + 3 \times 4 k - 3 \times 11

Factor out 2 k from the expression

2 k (4 k - 11) + 3 \times 4 k - 3 \times 11

Factor out 3 from the expression

2 k (4 k - 11) + 3 (4 k - 11)

Factor out 4 k - 11 from the expression

(2 k + 3) (4 k - 11)

(2 k + 3) (4 k - 11) = 0

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

2 k + 3 = 0 4 k - 11 = 0

Solve the equation for k

More Steps

Evaluate

2 k + 3 = 0

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

2 k = 0 - 3

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

2 k = - 3

Divide both sides

\frac{2 k}{2} = \frac{- 3}{2}

Divide the numbers

k = \frac{- 3}{2}

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

k = - \frac{3}{2}

k = - \frac{3}{2} 4 k - 11 = 0

Solve the equation for k

More Steps

Evaluate

4 k - 11 = 0

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

4 k = 0 + 11

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

4 k = 11

Divide both sides

\frac{4 k}{4} = \frac{11}{4}

Divide the numbers

k = \frac{11}{4}

k = - \frac{3}{2} k = \frac{11}{4}

Solution

k_{1} = - \frac{3}{2}, k_{2} = \frac{11}{4}

Alternative Form

k_{1} = - 1.5, k_{2} = 2.75

Show Solution