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

Question

Quizplus · Accepted Answer

To solve the quadratic equation $x^2 + 4x = 7$ by completing the square, first move the constant term to the other side: $x^2 + 4x - 7 = 0$. Then, add and subtract the square of half the coefficient of $x$ (which is $2^2 = 4$) on the left side to complete the square: $x^2 + 4x + 4 - 4 - 7 = 0$, 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 Quadratic Equation by Completing the Square x2+4x=7x ^ { 2 } + 4 x = 7x2+4x=7

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