Question

Need help with number eight. Need to solve each equation by completing the square

Answer 1

Given the algebraic equation

`v^2-12v+28=-7`

We are asked to solve the question using the completing the square method. This can be done with the following steps

Step-by-step explanation

Step 1: Take all the constant to the right hand side

`\begin{gathered} v^2-12v+28=-7 \\ v^2-12v=-7-28 \\ v^2-12v=-35 \end{gathered}`

Step 2: Add to both sides the square of half the coefficient of x

`\begin{gathered} v^2-12v+(-(12)/(2))^2=-35+(-(12)/(2))^2 \\ \end{gathered}`

Step 3: Factorize the left-hand sign and simplify the right-hand side.

`\begin{gathered} v^2-12v+(-(12)/(2))^2=-35+(-(12)/(2))^2 \\ v^2-12v+6^2=-35+6^2 \\ (v-6)^2=1 \end{gathered}`

Step 4: Find the square root of both sides

`\begin{gathered} \sqrt[]{(v-6)^2}=1 \\ v-6=\pm\sqrt[]{1} \\ v=6\pm\sqrt[]{1} \end{gathered}`

The solution to the equation is

Answer:

`v=7,\: v=5`