Solve the quadratic equation below by extracting square roots.Round to two decimal places.

Question

Quizplus · Accepted Answer

The quadratic equation is of the form $ax^2+bx+c=0$. Rearranging $6x^2-9x+6=0$, we get $x^2-\frac{3}{2}x+1=0$. We can now extract the square roots by using the formula:
$$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$
Plugging in the values, we get:
$$x=\frac{\frac{3}{2}\pm\sqrt{\left(\frac{3}{2}ight)^2-4(1)(1)}}{2(1)}=\frac{\frac{3}{2}\pm\frac{\sqrt{3}}{2}}{2}$$
Simplifying, we get:
$$x=\frac{3\pm\sqrt{3}}{4}$$
Rounding to two decimal places, we get:
$$x\approx 1.32 	ext{ or } 0.18$$
Option D is the only choice that matches one of these values, therefore it is the correct answer.

Solve the Quadratic Equation Below by Extracting Square Roots