Question

Solve the equation x(x+6) = 91 using completing the square, finding the square root, and solving. Put the equivalent equations in the appropriate order. |x+3 = 10 7 x² + 6x = 91 x= 7 or x = -13 x² - 6x +9 = 91 +9 x + 3 = 10 or x + 3 = -10 (x+3)² = 100

Answer 1

Given the equation below:

`x(x+6)=91`

Using the completing the square:

`\begin{gathered} x(x+6)=91 \\ x^2+6x-91=0 \\ half\text{ the coefficient of x, square and add to both side} \\ x^2+6x=91 \\ x^2+6x+(3)^2=91+(3)^2 \\ (x+3)^2=91+9 \\ (x+3)^2=100 \end{gathered}`

Square root both side of the equation

`\begin{gathered} (x+3)^2=100 \\ √((x+3)^2)=\pm√(100) \\ x+3=\pm10 \\ x=\pm10-3 \\ x=7,x=-13 \end{gathered}`

Therefore the equivalent equations in the appropriate order is