Question 1061654
.
solve the problem using quadratic equation 
x^2+x= a^2 +a 
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<U>Answer</U>. This equation has two and only two solutions: 1) x = a,  and 2) x = -1 -a.


<U>Solution</U>


<pre>
{{{x^2 + x}}} = {{{a^2 + a}}}   --->

{{{x^2 -a^2}}} = {{{a - x}}}  --->

(x+a)*(x-a) = -(x-a),   --->

(x+a)*(x-a) + (x-a) = 0   --->

(x+a+1)*(x-a) = 0   --->

Two solutions:

1.  x + a + 1 = 0,  or  x = -a-1,     OR/AND

2.  x = a.
</pre>

Solved.