Solve the quadratic equation by completing the square.
-$x ^ { 2 } - 9 x - 7 = 0$
A) $\frac { 9 \pm \sqrt { 109 } } { 2 }$
B) $\frac { 9 \pm 2 \sqrt { 7 } } { 2 }$
C) $9 \pm \sqrt { 109 }$
D) $\frac { - 9 \pm \sqrt { 109 } } { 2 }$

Question

Quizplus · Accepted Answer

To solve the quadratic equation $x^2 - 9x - 7 = 0$ by completing the square, first move the constant term to the other side: $x^2 - 9x = 7$. Then, to complete the square, add $\left(\frac{-9}{2}\right)^2 = \left(\frac{9}{2}\right)^2 = 20.25$ to both sides, resulting in $x^2 - 9x + 20.25 = 27.25$. This simplifies to $(x - \frac{9}{2})^2 = 27.25$. Taking the square root of both sides gives $x - \frac{9}{2} = \pm \sqrt{27.25}$, or $x = \frac{9}{2} \pm \sqrt{27.25}$. Simplifying $\sqrt{27.25}$ to $\sqrt{109}/2$, we get $x = \frac{9 \pm \sqrt{109}}{2}$, which matches choice A.

Solve the Quadratic Equation by Completing the Square x2−9x−7=0x ^ { 2 } - 9 x - 7 = 0x2−9x−7=0

Solve the Quadratic Equation by Completing the Square $x ^ { 2 } - 9 x - 7 = 0$