Question

Solve by completing the square. x2 - 8x + 5 = 0

Answer 1

Answer:

$\begin{gathered} x_1=4+\sqrt[]{11} \\ x_2=4-\sqrt[]{11} \end{gathered}$

Step-by-step explanation:

Solve the following quadratic completing the square:

$x^2-8x+5=0$

Keep x terms on the left and move the constant to the right side:

$x^2-8x=-5$

Then, take half of the x-term and square it.

$(-8\cdot\frac{1}{2})^2=16$

Now, add this result to both sides of the equation:

$x^2-8x+16=-5+16$

Rewrite the perfect square on the left.

$\begin{gathered} (x-4)^2=-5+16 \\ (x-4)^2=11 \end{gathered}$

Take the square root of both sides:

$\begin{gathered} \sqrt[]{(x-4)^2}=\pm\sqrt[]{11} \\ x-4=\pm\sqrt[]{11} \\ x=\pm\sqrt[]{11}+4 \end{gathered}$

Hence, the two solutions of the equation are:

$\begin{gathered} x_1=4+\sqrt[]{11} \\ x_2=4-\sqrt[]{11} \end{gathered}$