Solve 2x^(2)-3x-27

Question

Factor the expression

(x + 3) (2 x - 9)

Evaluate

2 x^{2} - 3 x - 27

Rewrite the expression

2 x^{2} + (- 9 + 6) x - 27

Calculate

2 x^{2} - 9 x + 6 x - 27

Rewrite the expression

x \times 2 x - x \times 9 + 3 \times 2 x - 3 \times 9

Factor out x from the expression

x (2 x - 9) + 3 \times 2 x - 3 \times 9

Factor out 3 from the expression

x (2 x - 9) + 3 (2 x - 9)

Solution

(x + 3) (2 x - 9)

Show Solution

x_{1} = - 3, x_{2} = \frac{9}{2}

Alternative Form

x_{1} = - 3, x_{2} = 4.5

Evaluate

2 x^{2} - 3 x - 27

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

2 x^{2} - 3 x - 27 = 0

Factor the expression

More Steps

Evaluate

2 x^{2} - 3 x - 27

Rewrite the expression

2 x^{2} + (- 9 + 6) x - 27

Calculate

2 x^{2} - 9 x + 6 x - 27

Rewrite the expression

x \times 2 x - x \times 9 + 3 \times 2 x - 3 \times 9

Factor out x from the expression

x (2 x - 9) + 3 \times 2 x - 3 \times 9

Factor out 3 from the expression

x (2 x - 9) + 3 (2 x - 9)

Factor out 2 x - 9 from the expression

(x + 3) (2 x - 9)

(x + 3) (2 x - 9) = 0

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

x + 3 = 0 2 x - 9 = 0

Solve the equation for x

More Steps

Evaluate

x + 3 = 0

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

x = 0 - 3

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

x = - 3

x = - 3 2 x - 9 = 0

Solve the equation for x

More Steps

Evaluate

2 x - 9 = 0

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

2 x = 0 + 9

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

2 x = 9

Divide both sides

\frac{2 x}{2} = \frac{9}{2}

Divide the numbers

x = \frac{9}{2}

x = - 3 x = \frac{9}{2}

Solution

x_{1} = - 3, x_{2} = \frac{9}{2}

Alternative Form

x_{1} = - 3, x_{2} = 4.5

Show Solution