Solve the quadratic equation by completing the square and applying the square root property. $$k ^ { 2 } + 14 k + 50 = 0$$
A) $\{ - 7 \pm i \}$
B) $\{ \pm i \}$
C) $\{ - 7 + i \}$
D) $\{ 7 + i \}$

Question

Quizplus · Accepted Answer

To solve the quadratic equation $k^2 + 14k + 50 = 0$ by completing the square, we first move the constant term to the other side: $k^2 + 14k = -50$. Then, we add $(\frac{14}{2})^2 = 49$ to both sides to complete the square: $k^2 + 14k + 49 = -50 + 49$, which simplifies to $(k + 7)^2 = -1$. Taking the square root of both sides gives $k + 7 = \pm i$, so $k = -7 \pm i$.

Solve the Quadratic Equation by Completing the Square and Applying k2+14k+50=0k ^ { 2 } + 14 k + 50 = 0k2+14k+50=0

Solve the Quadratic Equation by Completing the Square and Applying $k ^ { 2 } + 14 k + 50 = 0$