Question

value: 4
solve using the quadratic formula. round answers to the nearest hundredth.
$3x^2 - 9 = 7x$
a. $x \approx 2.45$ or $-0.11$
b. $x \approx 0.92$ or $-3.25$
c. $x \approx 9.09$ or $5.72$
d. $x \approx 3.25$ or $-0.92$

Explanation:

Step1: Rewrite to standard form

$3x^2 - 7x - 9 = 0$

Step2: Identify coefficients

$a=3$, $b=-7$, $c=-9$

Step3: Apply quadratic formula

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

Step4: Calculate discriminant

$\sqrt{(-7)^2 - 4(3)(-9)} = \sqrt{49 + 108} = \sqrt{157} \approx 12.53$

Step5: Compute two solutions

$x_1 = \frac{7 + 12.53}{6} \approx \frac{19.53}{6} \approx 3.25$
$x_2 = \frac{7 - 12.53}{6} \approx \frac{-5.53}{6} \approx -0.92$

Answer:

d. $x \approx 3.25$ or $-0.92$