Question

solve quadratic by completing the squarex^2 + 12x + 23 = 0which form do i use and solve(x+___)^2(x - ___) ^2solutionx = ___

Answer 1

Quadratics are in the general form:

`ax^2+bx+c`

For completing the square, we use:

`(x+(b)/(2))^2=c+((b)/(2))^2`

Now, we have:

`\begin{gathered} (x+(12)/(2))^2=-23+((12)/(2))^2 \\ (x+6)^2=-23+(6)^2 \\ (x+6)^2=13 \end{gathered}`

From here, we can easily solve for x with a little algebra. Shown below:

`\begin{gathered} \sqrt[]{(x+6)^2}=\pm\sqrt[]{13} \\ x+6=\pm\sqrt[]{13} \\ x=-6\pm\sqrt[]{13} \end{gathered}`

The answer(s) are:

`\begin{gathered} x=-6+\sqrt[]{13} \\ x=-6-\sqrt[]{13} \end{gathered}`

For further clarification

Form:

`(x+(12)/(2))^2=13`