Question

Solve the equation for all values of x by completing the square.x^2+ 8x = 9

Answer 1

Step 1

Given;

`x^2+8x=9`

Required; To find the value of x by completing the square

Step 2

Add half of the square of the coefficient of x to both sides

`\begin{gathered} coefficient\text{ of x=8} \\ \frac{1}{2\text{ }}of\text{ the square of the coefficient of x =\lparen}(8)/(2))^2 \end{gathered}`
`\frac{1}{2\text{ }}of\text{ the square of the coefficient of x=4}^2=\text{16}`

Hence we will have;

`\begin{gathered} x^2+8x+16=9+16 \\ x^2+8x+16=25 \end{gathered}`

Express the trinomial on the left side as a square of binomial.