Answer :
Answer:
Step-by-step explanation:
To solve the quadratic equation \(9x^2 - 7x + 2\), we can use the quadratic formula, which states that for an equation in the form \(ax^2 + bx + c = 0\), the solutions for \(x\) are given by:
\[x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}\]
In our equation, \(a = 9\), \(b = -7\), and \(c = 2\). Let's plug these values into the quadratic formula and solve for \(x\):
\[x = \frac{{-(-7) \pm \sqrt{{(-7)^2 - 4 \cdot 9 \cdot 2}}}}{{2 \cdot 9}}\]
\[x = \frac{{7 \pm \sqrt{{49 - 72}}}}{18}\]
\[x = \frac{{7 \pm \sqrt{{-23}}}}{18}\]
Since the discriminant (\(b^2 - 4ac\)) is negative, the square root of a negative number results in complex solutions. Thus, the solutions are imaginary.
\[x = \frac{{7 \pm \sqrt{{-23}}}}{18}\]