Question

Solve the equation by completing square method.

$d^2+10d=-9$

Short answer

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

Step-by-step solution

Given Information      

The Given equation is $d^2+10d=-9$.

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

The variable terms are on the left side.

$d^2+10d=-9$

Here $b=10$

So,

$$\begin{gathered} ={\left(\frac{1}{2}b\right)}^2 \\ ={\left(\frac{1}{2}\times 10\right)}^2 \\ ={\left(5\right)}^2=25 \end{gathered}$$

Add $25$to both sides.

$$\begin{gathered} d^2+10d+25=-9+25 \\ {d}^2+10d+25=16 \end{gathered}$$

Factor the perfect square trinomial as a binomial square.    

$(d+5{)}^2=16$

Use the square root property.

$$\begin{gathered} d+5=\pm \sqrt{16} \\ d+5=\pm 4 \end{gathered}$$

Solve for d.

$d=-5\pm 4$

Rewrite to show two solutions.

$$\begin{gathered} d=-5+4=-1 \\ d=-5-4=-9 \end{gathered}$$

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