What are the solutions to the following equation:

\(x^{2} + 8x + 15 = 0\)


A quadratic equation is any equation of the form:

\(y=ax^{2} + bx +c\) where a, b, and c are integers. The solutions to a quadratic equation are values that when substituted into the quadratic equation, yield a true statement.

One method for solving a quadratic equation is by factoring the equation and setting each of the factors equal to 0. Not all quadratic equations can be solved by factoring, and in such cases, it is necessary to use the quadratic formula to find the factors.

To simplify the quadratic equation given, two factors that multiply to 15 and add to 8 are necessary. The only valid pair of factors is 3 and 5. The equation can then be rewritten as: (x+3)(x+5)=0
Recall that if ab=0, then either a=0, or b=0. So, the values of x can be found by setting each parenthesis equal to 0 and solving for x:
 (x+3)=0   or   (x+5)=0
 x=−3   or   x=−5

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