SOLUTION: x^2+6X+7=0 Quadratic Formula

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Question 581610: x^2+6X+7=0
Quadratic Formula
Found 2 solutions by jim_thompson5910, josmiceli:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2%2B6x%2B7=0 Start with the given equation.


Notice that the quadratic x%5E2%2B6x%2B7 is in the form of Ax%5E2%2BBx%2BC where A=1, B=6, and C=7


Let's use the quadratic formula to solve for "x":


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%286%29+%2B-+sqrt%28+%286%29%5E2-4%281%29%287%29+%29%29%2F%282%281%29%29 Plug in A=1, B=6, and C=7


x+=+%28-6+%2B-+sqrt%28+36-4%281%29%287%29+%29%29%2F%282%281%29%29 Square 6 to get 36.


x+=+%28-6+%2B-+sqrt%28+36-28+%29%29%2F%282%281%29%29 Multiply 4%281%29%287%29 to get 28


x+=+%28-6+%2B-+sqrt%28+8+%29%29%2F%282%281%29%29 Subtract 28 from 36 to get 8


x+=+%28-6+%2B-+sqrt%28+8+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-6+%2B-+2%2Asqrt%282%29%29%2F%282%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%28-6%29%2F%282%29+%2B-+%282%2Asqrt%282%29%29%2F%282%29 Break up the fraction.


x+=+-3+%2B-+sqrt%282%29 Reduce.


x+=+-3%2Bsqrt%282%29 or x+=+-3-sqrt%282%29 Break up the expression.


So the solutions are x+=+-3%2Bsqrt%282%29 or x+=+-3-sqrt%282%29

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+x%5E2+%2B+6x+%2B+7+
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+1+
+b+=+6+
+c+=+7+
+x+=+%28-6+%2B-+sqrt%28+6%5E2-4%2A1%2A7+%29%29%2F%282%2A1%29+
+x+=+%28-6+%2B-+sqrt%28+36+-+28+%29%29+%2F+2+
+x+=+%28-6+%2B-+sqrt%28+8+%29%29+%2F+2+
+x+=+%28-6+%2B-+2%2Asqrt%28+2+%29%29+%2F+2+
+x+=+-3+%2B+sqrt%282%29+
and
+x+=+-3+-+sqrt%282%29+
-----------------
I'll check one solution, and you can
check the other
+%28+-3+%2B+sqrt%282%29%29%5E2+%2B+6%2A%28+-3+%2B+sqrt%282%29%29+%2B+7+=+0+
+9+-+6%2Asqrt%282%29+%2B+2+-+18+%2B+6%2Asqrt%282%29+%2B+7+=+0+
+9+%2B+2++-+18+%2B+7+=+0+
+18+-+18+=+0+
+0+=+0+
OK