Solve the equation by completing the square.
-$$x ^ { 2 } + 4 x - 9 = 0$$
A) $\{ - 2 - \sqrt { 13 } , - 2 + \sqrt { 13 } \}$
B) $\{ 2 + \sqrt { 13 } \}$
C) $\{ - 1 - \sqrt { 13 } , - 1 + \sqrt { 13 } \}$
D) $\{ - 2 - 1 \sqrt { 13 } , - 2 + 1 \sqrt { 13 } \}$

Question

Quizplus · Accepted Answer

First, we move the constant term to the right side of the equation: 
$$x ^ { 2 } + 4 x = 9$$
Next, we add and subtract the square of half of the coefficient of the $x$ term on the left side of the equation: 
$$x ^ { 2 } + 4 x + ( 2 ) ^ { 2 } - ( 2 ) ^ { 2 } = 9$$
Simplifying the left side and combining constants on the right, we have: 
$$( x + 2 ) ^ { 2 } - 13 = 0$$
Taking the square root of both sides and solving for $x+2$, we get: 
$$x + 2 = \pm \sqrt { 13 }$$
Solving for $x$ in each case, we get the answer to be $\{ - 2 - \sqrt { 13 } , - 2 + \sqrt { 13 } \}$.

Solve the Equation by Completing the Square x2+4x−9=0x ^ { 2 } + 4 x - 9 = 0x2+4x−9=0

Solve the Equation by Completing the Square $x ^ { 2 } + 4 x - 9 = 0$