Question

value: 4
solve using the quadratic formula. round answers to the nearest hundredth.
$6x^{2}-14x-9=0$
a. $x \approx 1.54$ or $0.79$
b. $x \approx 0.52$ or $-2.86$
c. $x \approx 15.69$ or $13.63$
d. $x \approx 2.86$ or $-0.52$

Explanation:

Step1: Identify quadratic coefficients

For $6x^2 -14x -9=0$, $a=6$, $b=-14$, $c=-9$

Step2: Recall quadratic formula

$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$

Step3: Calculate discriminant

$\Delta = (-14)^2 - 4(6)(-9) = 196 + 216 = 412$

Step4: Compute square root of discriminant

$\sqrt{412} \approx 20.2978$

Step5: Solve for positive root

$x_1 = \frac{14 + 20.2978}{12} \approx \frac{34.2978}{12} \approx 2.86$

Step6: Solve for negative root

$x_2 = \frac{14 - 20.2978}{12} \approx \frac{-6.2978}{12} \approx -0.52$

Answer:

d. $x \approx 2.86$ or $-0.52$