Question

Please help me Solve by rewriting the equation by completing the square :12x = 13 - x^2

Answer 1

x = -13 or 1.

Step-by-step explanation:

Given the equation:

`12x=13-x^2`

Follow the steps below to solve by completing the square method:

Step 1: Take the constant to the right-hand side.

`x^2+12x=13`

Step 2: Divide the coefficient of x by 2, square it and add it to both sides.

`x^2+12x+6^2=13+6^2`

Step 3: Write the left-hand side as a perfect square.

`\begin{gathered} (x+6)^2=13+36 \\ (x+6)^2=49 \end{gathered}`

Step 4: Take the square root of both sides.

`\begin{gathered} x+6=\pm\sqrt[]{49} \\ x+6=\pm7 \end{gathered}`

Step 5: Solve for x.

`\begin{gathered} x=-6\pm7 \\ \implies x=-6-7\text{ or }x=-6+7 \\ x=-13\text{ or }x=1 \end{gathered}`

The value of x is -13 or 1.