Chapter Closure
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If a second degree equation can be factored, we are able to rewrite the coefficient of the x-term as a sum of two numbers, a and b, whose product equals the constant.
x=- 3 and x=- 11.
To complete the square, we will write the equation on the form x^2+bx=c and then add the square of half of the coefficient to the x-term to both sides of the equation.
If a second degree equation can be factored, we are able to rewrite the coefficient of the x-term as a sum of two numbers, a and b, whose product equals the expression's constant.
y=x^2+(a+b)x+ab
⇕
y=(x+a)(x+b)
From the equation, we can identify what this sum and product must be.
y= 0
Use the Zero Product Property
(I): LHS-3=RHS-3
(II): LHS-11=RHS-11
To complete the square, we will write the equation on the form x^2+bx=c and then add the square of half the coefficient to the x-term to both sides of the equation.
LHS-33=RHS-33
LHS+(14/2)^2=RHS+(14/2)^2
Calculate quotient
Split into factors
a^2+2ab+b^2=(a+b)^2
Calculate power
Add terms
sqrt(LHS)=sqrt(RHS)
LHS-7=RHS-7
State solutions
As we can see, both methods gives the same answer.