Checkpoint: Solving to Complete the Square when 𝑎 ≠ 0, 1 Solution

Solving to Complete the Square when 𝑎 ≠ 0, 1 Solution

Solve by completing the square.

$2 x^{2} - 20 x + 74 = 0$

$\begin{array}{rcl} \frac{2}{2} x^{2} - \frac{20}{2} + \frac{74}{2} & = & \frac{0}{2} \\ x^{2} - 10 x + 37 & = & 0 \\ x^{2} - 10 x & = & - 37 \\ x^{2} - 10 x + {(\frac{- 10}{2})}^{2} & = & - 37 + {(\frac{- 10}{2})}^{2} \\ x^{2} - 10 x + {(- 5)}^{2} & = & - 37 + 25 \\ {(x - 5)}^{2} & = & - 12 \\ \sqrt{{(x - 5)}^{2}} & = & \pm \sqrt{- 12} \\ x - 5 & = & \pm i \sqrt{12} \\ x - 5 & = & \pm 2 i \sqrt{3} \\ x & = & 5 \pm 2 i \sqrt{3} \end{array}$

Note

Describe the steps as you complete them. This will help you master the process of solving by completing the square.