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}\frac{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.

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