Solve the equation by completing the square.
-$16 x ^ { 2 } - 3 x + 1 = 0$
A) $\left\{ \frac { 3 \pm i \sqrt { 55 } } { 32 } \right\}$
B) $\left\{ \frac { - 3 \pm i \sqrt { 55 } } { 32 } \right\}$
C) $\left\{ \frac { 3 - \mathrm { i } \sqrt { 55 } } { 32 } , \frac { - 3 + \mathrm { i } \sqrt { 55 } } { 32 } \right\}$
D) $\left\{ \frac { 3 \pm \sqrt { 55 } } { 32 } \right\}$

Question

Quizplus · Accepted Answer

To complete the square, add and subtract $\left(\frac{3}{32}\right)^2=\frac{9}{1024}$ to the left side of the equation:$$16x^2-3x+1=\frac{9}{1024}$$$$16x^2-3x+\frac{9}{1024}=\frac{9}{1024}+\frac{9}{1024}$$$$(4x-\frac{3}{32})^2=\frac{18}{1024}$$$$4x-\frac{3}{32}=\pm\sqrt{\frac{18}{1024}}$$$$4x=\frac{3}{32}\pm\frac{3\sqrt{2}}{32}$$$$x=\frac{3\pm3\sqrt{2}}{32\cdot4}$$$$x=\frac{3\pm3\sqrt{2}}{128}$$$$x=\frac{3\pm\sqrt{55}}{128}$$$$x=\frac{3\pm i\sqrt{55}}{32}$$

Solve the Equation by Completing the Square 16x2−3x+1=016 x ^ { 2 } - 3 x + 1 = 016x2−3x+1=0

Solve the Equation by Completing the Square $16 x ^ { 2 } - 3 x + 1 = 0$