Solve the equation by completing the square.
-$$x ^ { 2 } + 4 x - 7 = 0$$
A) $\{ - 2 - \sqrt { 11 } , - 2 + \sqrt { 11 } \}$
B) $\{ - 2 - 1 \sqrt { 11 } , - 2 + 1 \sqrt { 11 } \}$
C) $\{ - 1 - \sqrt { 11 } , - 1 + \sqrt { 11 } \}$
D) $\{ 2 + \sqrt { 11 } \}$

Question

Quizplus · Accepted Answer

To solve the equation $x^2 + 4x - 7 = 0$ by completing the square, first move the constant term to the other side: $x^2 + 4x = 7$. Then, add $(\frac{4}{2})^2 = 4$ to both sides to complete the square: $x^2 + 4x + 4 = 11$. This gives $(x + 2)^2 = 11$, so $x + 2 = \pm \sqrt{11}$, leading to $x = -2 \pm \sqrt{11}$.

Solve the Equation by Completing the Square x2+4x−7=0x ^ { 2 } + 4 x - 7 = 0x2+4x−7=0

Solve the Equation by Completing the Square $x ^ { 2 } + 4 x - 7 = 0$