CEMC Fermat

Algebra Difficulty 2.5 Junior Find the answer

If $x=18$ is one of the solutions of the equation $x^{2}+12x+c=0$ , what is the other solution of this equation?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Since $x=18$ is a solution to the equation $x^{2}+12x+c=0$ , then $x=18$ satisfies this equation. Thus, $18^{2}+12(18)+c=0$ and so $324+216+c=0$ or $c=-540$ . Therefore, the original equation becomes $x^{2}+12x-540=0$ or $(x-18)(x+30)=0$ . Therefore, the other solution is $x=-30$ .

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