Maintaining Mathematical Proficiency
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To complete the square, make sure all the variable terms are on one side of the equation. Then, divide both sides of the equation by a so the coefficient of z^2 is 1.
z=1
We want to solve the quadratic equation by completing the square. Note that all terms with z are on one side of the equation.
- z^2+ 2z=1
Now let's divide each side by - 1 so the coefficient of z^2 will be 1.
.LHS /- 1.=.RHS /- 1.
Write as a sum of fractions
a* b/c=a/c* b
Calculate quotient
In a quadratic expression, b is the linear coefficient. For the equation above, we have that b=- 2. Let's now calculate ( b2 )^2.
Next, we will add ( b2 )^2=1 to both sides of our equation. Then, we will factor the trinomial on the left-hand side and solve the equation.
LHS+1=RHS+1
a^2-2ab+b^2=(a-b)^2
Add terms
sqrt(LHS)=sqrt(RHS)
Calculate root
LHS+1=RHS+1
The solution of the equation is z=1.