Answer :
Answer:
x = -0.21, 0.54
Explanation:
The quadratic formula says that if we have a quadratic equation of the form
[tex]ax^2+bx+c=0^{}[/tex]then the value of x is given by
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]Now in our case, we have
[tex]9x^2-3x-1=0[/tex]therefore, for the quadratic formula we put a = 9, b = -3, and c = -1 to get
[tex]x=\frac{3\pm\sqrt[]{3^2-4(9)(-1)}}{2(9)}[/tex]which simplifies to give
[tex]x=\frac{3\pm3\sqrt[]{5}}{18}[/tex][tex]\begin{gathered} x=\frac{1}{6}-\frac{\sqrt[]{5}}{6}\approx-0.21 \\ x=\frac{1}{6}+\frac{\sqrt[]{5}}{6}\approx0.54 \end{gathered}[/tex]Hence, rounded to the nearest hundreth, the solutions to the quadratic equation are
x = -0.21 and x = 0.54.