Question

Solve the equation using the Complete The Square Methodx^2+12x=13Do your work on paper. Take a picture, and upload it here. Show all your work/steps.

Answer 1

Given the quadratic equation:

$x^2+12x=13$

We can rewrite the equation as follows:

$\begin{gathered} x^2+12x-13=0 \\ x^2+2\cdot6\cdot x-13=0 \\ x^2+2\cdot6\cdot x+6^2-6^2-13=0 \\ (x^2+2\cdot6\cdot x+6^2)-36-13=0 \end{gathered}$

We see that the term inside the parenthesis is a perfect square polynomial. Then:

$(x+6)^2-49=0$

Solving for x:

$(x+6)^2=49$

Taking the square on both sides:

$\begin{gathered} \sqrt{(x+6)^2}=\sqrt{49} \\ \\ |x+6|=7 \end{gathered}$

This equation can turn into two equations:

$\begin{gathered} x+6=7...(1) \\ x+6=-7...(2) \end{gathered}$

Solving (1):

$\begin{gathered} x=7-6 \\ \\ \Rightarrow x=1 \end{gathered}$

Solving (2):

$\begin{gathered} x=-7-6 \\ \\ \Rightarrow x=-13 \end{gathered}$

Finally, the solutions to the equation are:

$\begin{gathered} x_1=1 \\ \\ x_2=-13 \end{gathered}$