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

$\sqrt{(-7)^2-4(3)(-9)}=\sqrt{49+108}=\sqrt{157}\approx12.53$

Step5: Compute two roots

$x_1=\frac{7+12.53}{6}\approx\frac{19.53}{6}\approx3.25$
$x_2=\frac{7-12.53}{6}\approx\frac{-5.53}{6}\approx-0.92$

Answer:

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