Solve the equation by completing the square.
-$$\frac { x ^ { 2 } } { 16 } + x + \frac { 21 } { 8 } = 0$$
A) $$8 + \sqrt { 22 }$$
B) $$- 16 \pm \sqrt { 42 }$$
C) $$- 8 \pm \sqrt { 22 }$$
D) $$8 - \sqrt { 42 } , 8 + \sqrt { 42 }$$

Question

Quizplus · Accepted Answer

To solve the equation by completing the square, we first need to express the equation in the form $ax^2 + bx + c = 0$. The given equation is already in this form: $\frac{x^2}{16} + x + \frac{21}{8} = 0$.Next, we want to complete the square for the quadratic part of the equation. To do this, we need to make the coefficient of $x^2$ equal to 1 (if it's not already). In this case, we can multiply the entire equation by 16 to get rid of the fraction:$$x^2 + 16x + 42 = 0$$Now, to complete the square, we take the coefficient of $x$ (which is 16), divide it by 2, and square it. This gives us $(16/2)^2 = 8^2 = 64$. We add and subtract this number inside the equation to complete the square:$$x^2 + 16x + 64 - 64 + 42 = 0$$This simplifies to:$$(x + 8)^2 - 22 = 0$$Now, we solve for $x$:$$(x + 8)^2 = 22$$Taking the square root of both sides:$$x + 8 = \pm \sqrt{22}$$Finally, solving for $x$:$$x = -8 \pm \sqrt{22}$$Therefore, the correct answer is $$-8 \pm \sqrt{22}$$, which corresponds to choice C.

Solve the Equation by Completing the Square x216+x+218=0\frac { x ^ { 2 } } { 16 } + x + \frac { 21 } { 8 } = 016x2​+x+821​=0

Solve the Equation by Completing the Square $\frac { x ^ { 2 } } { 16 } + x + \frac { 21 } { 8 } = 0$