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:

$(x+\frac{b}{2})^2=c+(\frac{b}{2})^2$

Now, we have:

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

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:

$(x+\frac{12}{2})^2=13$