Question

5.3 - online quiz - solving quadratic equations
started: dec 12 at 6:18pm
quiz instructions
question 4
solve the following equation by factoring.
$10x^2 - 20x = 3x - 12$
○ $x = 5/4$, $x = 2/3$
○ $x = 4/5$, $x = 3/2$
○ $x = -5/4$, $x = -2/3$
○ $x = -4/5$, $x = -3/2$

Explanation:

Step1: Rearrange the equation

Move all terms to the left side: \(10x^{2}-20x - 3x + 12 = 0\), simplify to \(10x^{2}-23x + 12 = 0\).

Step2: Factor the quadratic

Find two numbers that multiply to \(10\times12 = 120\) and add to \(-23\). The numbers are \(-8\) and \(-15\). Rewrite the middle term: \(10x^{2}-8x - 15x + 12 = 0\). Group and factor: \(2x(5x - 4)-3(5x - 4)=0\), so \((2x - 3)(5x - 4)=0\).

Step3: Solve for x

Set each factor to zero: \(2x - 3 = 0\) gives \(x=\frac{3}{2}\), \(5x - 4 = 0\) gives \(x=\frac{4}{5}\).

Answer:

\(x = \frac{4}{5}\), \(x = \frac{3}{2}\) (corresponding to the option: \(x = 4/5, x = 3/2\))