Solve the equation by completing the square.
-$$x ^ { 2 } + 14 x + 26 = 0$$
A) $\{ - 7 - \sqrt { 23 } , - 7 + \sqrt { 23 } \}$
B) $\{ - 14 + \sqrt { 26 } \}$
C) $\{ 7 + \sqrt { 23 } \}$
D) $\{ 7 - \sqrt { 26 } , 7 + \sqrt { 26 } \}$

Question

Quizplus · Accepted Answer

To solve the equation $x^2 + 14x + 26 = 0$ by completing the square, we first move the constant term to the other side: $x^2 + 14x = -26$. Then, we add $(\frac{14}{2})^2 = 49$ to both sides to complete the square: $x^2 + 14x + 49 = 23$, which simplifies to $(x + 7)^2 = 23$. Taking the square root of both sides gives $x + 7 = \pm\sqrt{23}$, leading to $x = -7 \pm \sqrt{23}$.

Solve the Equation by Completing the Square x2+14x+26=0x ^ { 2 } + 14 x + 26 = 0x2+14x+26=0

Solve the Equation by Completing the Square $x ^ { 2 } + 14 x + 26 = 0$