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If you complete the square on the equation
x^2 + 10x = 9 + 4x,

you will get an equation of the form "(x + r)^2 = c". Enter this equation.

 May 23, 2022
 #1
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We first move all terms to the left-hand side.

 

\(x^2 + 10x - 4x - 9= 0 \\ x^2 + 6x - 9= 0\)

 

We want to make (x + r)^2 on the left-hand side, and we know that (x + 3)^2 = x^2 + 6x + 9. What if we add 18 to both sides?

 

\(x^2 + 6x + 9 = 18\)

 

Now just write the left-hand side as (x + 3)^2 and there's the answer.

 May 23, 2022

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