solve the quadratic equation.\n2x² - 7x + 9 = 0\nwrite one exact solution in each box. you can add or remove…

Explanation:

Step1: Identify coefficients

For the quadratic equation $2x^{2}-7x + 9=0$, we have $a = 2$, $b=-7$, $c = 9$.

Step2: Calculate the discriminant

The discriminant $\Delta=b^{2}-4ac=(-7)^{2}-4\times2\times9=49 - 72=-23$.

Step3: Use the quadratic - formula

The quadratic formula is $x=\frac{-b\pm\sqrt{\Delta}}{2a}$. Since $\Delta=-23<0$, the solutions are complex numbers. $x=\frac{7\pm\sqrt{- 23}}{4}=\frac{7\pm i\sqrt{23}}{4}$.

Answer:

$x=\frac{7 + i\sqrt{23}}{4}$, $x=\frac{7 - i\sqrt{23}}{4}$