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What is the sum of all possible values of for which x^2 + kx - 10x + 36 -32  is the square of a binomial?

 May 18, 2022
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We can simplify this equation to: \(x^2 + kx- 10x + 4\).

 

Factoring out x gives us: \(x^2 + x(k-10) +4\)

 

For the quadratic to have only 1 solution, the discriminant(\(b^2 - 4ac\)) must be equal to 0. 

 

Substituting what we know, we have: \((k-10)^2 - 16 = 0\)

 

Adding 16 to both sides gives us: \((k-10)^2 = 16\)

 

Taking the square root of both sides gives us: \(k - 10 = \pm 4\).

 

Now, we can find the 2 values of \(k\) and add them up. 

 

Can you take it from here?

 May 18, 2022

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