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# Algebra

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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