Solve the equation by completing the square.
-$$x ^ { 2 } + 10 x + 6 = 0$$
A) $\{ 5 - \sqrt { 6 } , 5 + \sqrt { 6 } \}$
B) $\{ - 10 + \sqrt { 6 } \}$
C) $\{ 5 + \sqrt { 19 } \}$
D) $\{ - 5 - \sqrt { 19 } , - 5 + \sqrt { 19 } \}$

Question

Quizplus · Accepted Answer

To solve the equation $x^2 + 10x + 6 = 0$ by completing the square, first move the constant term to the other side: $x^2 + 10x = -6$. Then, add $(\frac{10}{2})^2 = 25$ to both sides to complete the square: $x^2 + 10x + 25 = 19$, which simplifies to $(x + 5)^2 = 19$. Taking the square root of both sides gives $x + 5 = \pm\sqrt{19}$, leading to the solutions $x = -5 \pm \sqrt{19}$.

Solve the Equation by Completing the Square x2+10x+6=0x ^ { 2 } + 10 x + 6 = 0x2+10x+6=0

Solve the Equation by Completing the Square $x ^ { 2 } + 10 x + 6 = 0$