Solve the equation by completing the square.
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Question

Quizplus · Accepted Answer

The equation is not in standard form, so we need to group the x terms and constant terms separately. $2x^2+8x=-5$ can be rewritten as $2(x^2+4x)=-5$. To complete the square, we need to add and subtract $(4/2)^2=4$ inside the parentheses, giving $2(x^2+4x+4-4)=-5$. Simplifying this gives $2((x+2)^2-4)=-5$. Dividing both sides by 2 gives $(x+2)^2-4=-5/2$. Adding 4 to both sides gives $(x+2)^2=3/2$, and taking the square root yields $x+2=\pm\sqrt{3/2}$. Subtracting 2 from both sides gives the solutions $x=-2\pm\sqrt{3/2}$. Therefore, the correct answer is B. To complete the square for the given equation, we need to add and subtract the square of half of the coefficient of the term with the variable. 
Here, the given equation is: 
$x^2+14x+47=0$
To complete the square, we need to add and subtract $(14/2)^2=49$ to the equation. 
$x^2+14x+47+49-49=0$
$(x+7)^2=2$
$x+7=\pm\sqrt{2}$
$x=-7\pm\sqrt{2}$
Therefore, option B is the correct answer.

Solve the Equation by Completing the Square