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The quadratic -6x^2+72x+216 can be written in the form a(x+b)^2+c, where a, b, and c are constants. What is a+b+c?

 Jun 27, 2022

Best Answer 

 #1
avatar+2222 
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Note that \((x+b)^2 = x^2 + b^2 + 2xb\)

 

This means that \(a = -6\)

 

Also, note that \(-6 \times 2xb = 72x\), because it is the only term with x. 

 

This means \(b = -6\)

 

Expanding what we have gives us: \(-6x^2 + 72x -216\), so we add 432, to make the constant positive. 

 

This means \(a + b + c = \color{brown}\boxed{420}\)

 Jun 27, 2022
 #1
avatar+2222 
+1
Best Answer

Note that \((x+b)^2 = x^2 + b^2 + 2xb\)

 

This means that \(a = -6\)

 

Also, note that \(-6 \times 2xb = 72x\), because it is the only term with x. 

 

This means \(b = -6\)

 

Expanding what we have gives us: \(-6x^2 + 72x -216\), so we add 432, to make the constant positive. 

 

This means \(a + b + c = \color{brown}\boxed{420}\)

BuilderBoi Jun 27, 2022

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