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Prealgebra and Introductory Algebra

For a quadratic equation of the form $x^{2}+b x+c=0,$ the sum of the solutions is equal to the opposite of $b$, and the product of the solutions is equal to $c .$ For example, the solutions of the equation $x^{2}+5 x+6=0$ are $-2$ and $-3 .$ The sum of the solutions is

$-5,$ the opposite of the coefficient of $x$. The product of the solutions is $6,$ the constant term. This is one way to check the solutions of a quadratic equation. Use this method to determine whether the given numbers are solutions of the equation. If they are not solutions of the equation, find the solutions.

$$x^{2}-8 x-14=0 ;-4+\sqrt{15} \text { and }-4-\sqrt{15}$$