Solve the equation $x ^ { 2 } - 4 x - 3 = 0$ by completing the square. Give the solutions in exact form and in decimal form rounded to two decimal places. (The solutions may be complex numbers.)
A) $4 + \sqrt { 7 } i \approx 4 + 2.65 i$ ; $4 - \sqrt { 7 } i \approx 4 - 2.65 i$
B) $2 + \sqrt { 7 } i \approx 2 + 2.65 i$ ; $2 - \sqrt { 7 } i \approx 2 - 2.65 i$
C) $4 + \sqrt { 7 } \approx 6.65$ ; $4 - \sqrt { 7 } \approx 1.35$
D) $2 + \sqrt { 7 } \approx 4.65$ ; $2 - \sqrt { 7 } \approx - 0.65$
E) $- 2 + \sqrt { 7 } \approx 0.65$ ; $- 2 - \sqrt { 7 } \approx - 4.65$

Question

Quizplus · Accepted Answer

Completing the square for the equation $x^2 - 4x - 3 = 0$, we get $(x - 2)^2 = 7$. Solving for $x$, we find $x = 2 \pm \sqrt{7}$. The decimal approximations are $2 + \sqrt{7} \approx 4.65$ and $2 - \sqrt{7} \approx -0.65$.

Solve the Equation x2−4x−3=0x ^ { 2 } - 4 x - 3 = 0x2−4x−3=0

Solve the Equation $x ^ { 2 } - 4 x - 3 = 0$