Solve 2x^2 - 3x - 9 - Socratic AI (ScanMath)

Question

Factor the expression

(x - 3) (2 x + 3)

Evaluate

2 x^{2} - 3 x - 9

Rewrite the expression

2 x^{2} + (3 - 6) x - 9

Calculate

2 x^{2} + 3 x - 6 x - 9

Rewrite the expression

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

Factor out x from the expression

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

Factor out - 3 from the expression

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

Solution

(x - 3) (2 x + 3)

Show Solution

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

Alternative Form

x_{1} = - 1.5, x_{2} = 3

Evaluate

2 x^{2} - 3 x - 9

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

2 x^{2} - 3 x - 9 = 0

Factor the expression

More Steps

Evaluate

2 x^{2} - 3 x - 9

Rewrite the expression

2 x^{2} + (3 - 6) x - 9

Calculate

2 x^{2} + 3 x - 6 x - 9

Rewrite the expression

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

Factor out x from the expression

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

Factor out - 3 from the expression

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

Factor out 2 x + 3 from the expression

(x - 3) (2 x + 3)

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

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

x - 3 = 0 2 x + 3 = 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 + 3 = 0

Solve the equation for x

More Steps

Evaluate

2 x + 3 = 0

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

2 x = 0 - 3

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

2 x = - 3

Divide both sides

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

Divide the numbers

x = \frac{- 3}{2}

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

x = - \frac{3}{2}

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

Solution

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

Alternative Form

x_{1} = - 1.5, x_{2} = 3

Show Solution