SOLUTION: solve the problem using quadratic equation x^2+x= a^2 +a

Algebra ->  Finance -> SOLUTION: solve the problem using quadratic equation x^2+x= a^2 +a       Log On


   

Question 1061654: solve the problem using quadratic equation
x^2+x= a^2 +a
Found 3 solutions by solver91311, josmiceli, ikleyn:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!








Here, , and

So:



Simplify to find the two values of in terms of

John

My calculator said it, I believe it, that settles it

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
To avoid confusion, I'll use capital A
+x%5E2+%2B+x+=+A%5E2+%2B+A+
+x%5E2+%2B+x+-+%28+A%5E2+%2B+A+%29+=+0+
+x+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+1+
+b+=+1+
+c+=+A%5E2+%2B+A+
+x+=+%28+-1+%2B-+sqrt%28+1%5E2+-+4%2A1%2A%28A%5E2+%2B+A%29+%29%29%2F%282%2A1%29+
+x+=+%28+-1+%2B-+sqrt%28+1+-+4%2A%28A%5E2+%2B+A%29+%29%29%2F2+
+x+=+%28+-1+%2B-+sqrt%28+1+-+4A%5E2+-+4A%29+%29%29%2F2+
+x+=+%28+-1+%2B-+sqrt%28+-+4A%5E2+-+4A+%2B+1+%29+%29%29%2F2+
Check my math & maybe get another opinion
---------------------------------------

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
solve the problem using quadratic equation
x^2+x= a^2 +a
~~~~~~~~~~~~~~~~~~~~~

Answer. This equation has two and only two solutions: 1) x = a, and 2) x = -1 -a.

Solution 

x%5E2+%2B+x = a%5E2+%2B+a   --->

x%5E2+-a%5E2 = 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.

Solved.