Solve the equation by completing the square.
-$$x ^ { 2 } + 6 x - 40 = 0$$
A) $\{ - 4,10 \}$
B) $\{ - 30 , - 10 \}$
C) $\{ \pm \sqrt { - 40 } \}$
D) $\{ 4 , - 10 \}$

Question

Quizplus · Accepted Answer

To complete the square, we need to add and subtract $(6/2)^2 = 9$ inside the left side:
$$x ^ { 2 } + 6 x + 9 - 9- 40 = (x+3)^2-49= 0$$
Adding $49$ on both sides yields:
$$(x+3)^2=49 \implies x+3=\pm 7 \implies x=-3\pm 7$$
Thus, the solutions are $\{-10, 4\}$. Therefore, the answer is choice D.

Solve the Equation by Completing the Square x2+6x−40=0x ^ { 2 } + 6 x - 40 = 0x2+6x−40=0

Solve the Equation by Completing the Square $x ^ { 2 } + 6 x - 40 = 0$