Questions: Use the quadratic formula to solve for x. 9x^2 - 3x = 1 Round your answer to the nearest hundredth. If there is more than one solution, separate them with commas. x=

Use the quadratic formula to solve for x.

9x^2 - 3x = 1

Round your answer to the nearest hundredth. If there is more than one solution, separate them with commas.

x=

Transcript text: Use the quadratic formula to solve for $x$. \[ 9 x^{2}-3 x=1 \] Round your answer to the nearest hundredth. If there is more than one solution, separate them with commas. \[ x= \] $\square$

Solution

Solution Steps

Step 1: Identify the coefficients

The coefficients are $a = 9$, $b = -3$, and $c = -1$.

Step 2: Calculate the discriminant

The discriminant $\Delta$ is calculated as $\Delta = b^2 - 4ac = -3^2 - 4_9_-1 = 45$.

Step 3: Since the discriminant is positive, there are two distinct real roots.

Step 4: Calculate the roots using the quadratic formula

The roots are calculated using the formula $x = \frac{-b \pm \sqrt{\Delta}}{2a}$. Substituting the values, we get $x_1 = (0.54+0j)$ and $x_2 = (-0.21+0j)$.