Question

Solved it quadratic equation by completing the square.x^2-14x+46=0First choose the appropriate form and fill in the blanks with the correct numbers. Then solve the equation. If there’s more than one solution, separate them with commas.

Answer 1

Let's comple the squares of the equation:

$\begin{gathered} x^2-14x+46=0 \\ x^2-14x=-46 \\ x^2-14x+(\frac{14}{2})^2=(\frac{14}{2})^2-46 \\ x^2-14x+49=49-46 \\ (x-7)^2=3 \end{gathered}$

Hence the correct form is:

$(x-7)^2=3$

Let's solve the last equation:

$\begin{gathered} (x-7)^2=3 \\ x-7=\pm\sqrt[]{3} \\ x=7\pm\sqrt[]{3} \end{gathered}$

Thefore the solutions of the equation are:

$\begin{gathered} x=7+\sqrt[]{3} \\ x=7-\sqrt[]{3} \end{gathered}$