using the quadratic formula to solve 2x² = 4x - 7, what are the values of x?\n2±√10i\n1±√10i\n(2±√10i)/2\n1±√…

Explanation:

Step1: Rewrite the equation in standard form

First, rewrite $2x^{2}=4x - 7$ as $2x^{2}-4x + 7=0$. For a quadratic equation $ax^{2}+bx + c = 0$, here $a = 2$, $b=-4$, $c = 7$.

Step2: Apply the quadratic formula

The quadratic formula is $x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. Substitute $a = 2$, $b=-4$, $c = 7$ into it. We get $x=\frac{-(-4)\pm\sqrt{(-4)^{2}-4\times2\times7}}{2\times2}=\frac{4\pm\sqrt{16 - 56}}{4}=\frac{4\pm\sqrt{- 40}}{4}$.

Step3: Simplify the square - root term

Since $\sqrt{-40}=\sqrt{40}\times\sqrt{-1}=2\sqrt{10}i$, then $x=\frac{4\pm2\sqrt{10}i}{4}=\frac{2\pm\sqrt{10}i}{2}$.

Answer:

C. $\frac{2\pm\sqrt{10}i}{2}$