Question

solve the equation.
\\x(2x - 3) = 9\\

\\(x = \\)
(use a comma to separate answers as needed.)

Explanation:

⚡ Using what you learned: factoring and solving quadratic equations

Step 1: Distribute and set to zero

$$ x(2x - 3) = 9 $$

$$ 2x^2 - 3x - 9 = 0 $$

Step 2: Factor the quadratic equation

Find two numbers that multiply to \(2 \times (-9) = -18\) and add to \(-3\). These numbers are \(-6\) and \(3\).

$$ 2x^2 - 6x + 3x - 9 = 0 $$

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

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

Step 3: Solve for \(x\)

$$ 2x + 3 = 0 \implies x = -\frac{3}{2} $$

$$ x - 3 = 0 \implies x = 3 $$

Answer:

\(-\frac{3}{2}, 3\)