Question

Some the quadratic equation by completing the square.X^2-4x-10=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

Given:

$x^2-4x-10=0$

To find the roots by completing the square methods:

The given equation can be written as,

$x^2-4x=10$

Add 4 on both sides, we get

$\begin{gathered} x^2-4x+4=10+4 \\ x^2-4x+2^2=14 \\ (x-2)^2=14 \\ x-2=\pm\sqrt[]{14} \\ x=\pm\sqrt[]{14}+2 \end{gathered}$

Hence, the form is,

$(x-2)^2=14$

And the solution is,

$x=\sqrt[]{14}+2,-\sqrt[]{14}+2$