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

Question

Quizplus · Accepted Answer

To solve the equation by completing the square, first move all terms to one side: $x^2 + 4x - 7 = 0$. Then, add $(\frac{4}{2})^2 = 4$ to both sides to complete the square: $x^2 + 4x + 4 = 11$, which simplifies to $(x + 2)^2 = 11$. Taking the square root of both sides gives $x + 2 = \pm \sqrt{11}$, so $x = -2 \pm \sqrt{11}$.

Solve the Equation by Completing the Square x2=7−4xx ^ { 2 } = 7 - 4 xx2=7−4x

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