Solve 2x^2 - 9x - 11

Question

Factor the expression

(x + 1) (2 x - 11)

Evaluate

2 x^{2} - 9 x - 11

Rewrite the expression

2 x^{2} + (- 11 + 2) x - 11

Calculate

2 x^{2} - 11 x + 2 x - 11

Rewrite the expression

x \times 2 x - x \times 11 + 2 x - 11

Factor out x from the expression

x (2 x - 11) + 2 x - 11

Solution

(x + 1) (2 x - 11)

Show Solution

x_{1} = - 1, x_{2} = \frac{11}{2}

Alternative Form

x_{1} = - 1, x_{2} = 5.5

Evaluate

2 x^{2} - 9 x - 11

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

2 x^{2} - 9 x - 11 = 0

Factor the expression

More Steps

Evaluate

2 x^{2} - 9 x - 11

Rewrite the expression

2 x^{2} + (- 11 + 2) x - 11

Calculate

2 x^{2} - 11 x + 2 x - 11

Rewrite the expression

x \times 2 x - x \times 11 + 2 x - 11

Factor out x from the expression

x (2 x - 11) + 2 x - 11

Factor out 2 x - 11 from the expression

(x + 1) (2 x - 11)

(x + 1) (2 x - 11) = 0

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

x + 1 = 0 2 x - 11 = 0

Solve the equation for x

More Steps

Evaluate

x + 1 = 0

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

x = 0 - 1

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

x = - 1

x = - 1 2 x - 11 = 0

Solve the equation for x

More Steps

Evaluate

2 x - 11 = 0

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

2 x = 0 + 11

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

2 x = 11

Divide both sides

\frac{2 x}{2} = \frac{11}{2}

Divide the numbers

x = \frac{11}{2}

x = - 1 x = \frac{11}{2}

Solution

x_{1} = - 1, x_{2} = \frac{11}{2}

Alternative Form

x_{1} = - 1, x_{2} = 5.5

Show Solution