Question

Solve the equation by completing square method.

$d^2-8d=9$

Short answer

The solutions are$d=-1,d=9$

Step-by-step solution

Given Information.  

The Given equation is $d^2-8d=9$.

Isolate the variable terms on one side and the constant terms on the other. 

The variable terms are on the left side.

$d^2-8d=9$

Here,$b=-8$.

Find 12b2and add to the both sides of equation.

$$\begin{gathered} ={\left(\frac{1}{2}(-8)\right)}^2 \\ ={\left(-4\right)}^2 \\ =16 \end{gathered}$$

Add $16$both sides.

$$\begin{gathered} d^2-8d+16=9+16 \\ {d}^2-8d+16=25 \end{gathered}$$

Factor the perfect square trinomial as a binomial square. 

$(d-4{)}^2=25$

Use the square root property.

$$\begin{gathered} d-4=\pm \sqrt{25} \\ d-4=\pm 5 \\ d=4\pm 5 \end{gathered}$$

Rewrite to show two solutions.

$$\begin{gathered} d=4\pm 5 \\ d=4+5=9 \end{gathered}$$

The solutions are$d=-1,d=9$

Check the solutions. 

Substitute $d=-1$.

$$\begin{gathered} d^2-8d=9 \\ (-1{)}^2-8(-1)\stackrel{?}{=}9 \\ 1+8\stackrel{?}{=}9 \\ 9=9True \end{gathered}$$

Substitute $d=9$.

$$\begin{gathered} d^2-8d=9 \\ (9{)}^2-8(9)\stackrel{?}{=}9 \\ 81-72\stackrel{?}{=}9 \\ 9=9True \end{gathered}$$

Thus, the solutions are$d=-1,d=9$