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

User Galdo
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1 Answer

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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

User Edward Ruchevits
by
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