Question 1193600
<br>
{{{x^2+15x=-50}}}<br>
(1) Get all terms on one side of the equation (add 50 to both sides):<br>
{{{x^2+15x+50=0}}}<br>
(2) You want to factor this as the product of two linear expressions.  The constant term is positive, so the signs of the two expressions are the same; and the linear term is positive, so the signs of the two expressions are both positive.  So the factoring will be of the form<br>
{{{(x+a)(x+b)=x^2+(a+b)x+ab=x^2+15x+50}}}<br>
So you want a and b to be two positive integers whose sum is 15 and whose product is 50 -- 5 and 10.  So<br>
{{{x^2+15x+50=(x+5)(x+10)=0}}}
The product is 0 if and only if one of the factors is 0:<br>
{{{x+5=0}}} --> {{{x=-5}}} or {{{x+10=0}}} --> {{{x=-10}}}<br>
ANSWERS: x=-5 and x=-10<br>