Set the binomial equal to 0, then set aside the constant value 10 and replace it with c.
Find a value for c that completes the square.0=x2+6x+c
Since x is on the right side of the equation, switch the sides so it is on the left side of the equation.x^2+6x=0
To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of b, the coefficient of x.(b/2)^2=(3)^2
Add the term to each side of the equation.x^+6x+(3)2=0+(−3)2
Simplify the equation.
x^2+6x+9=9
Factor the perfect trinomial square into (x+3)^2.(x+3)^2=9
Move the new constant to the left side of the equation.(x+3)^2+(9)=0
Add the original constant to the new constant.(x+3)^2+(9)+(10)=0
Complete the square in the expression x^2+6x+10.(x+3)^2+1
Reorder the right side of the equation to match the vertex form of a parabola.y=(x+3)^2+1