SOLUTION: 2x^2+8x+15=0

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Question 156718: 2x^2+8x+15=0
Found 3 solutions by jim_thompson5910, oscargut, josmiceli:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
2x%5E2%2B8x%2B15=0 Start with the given equation.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=2, b=8, and c=15


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-%288%29+%2B-+sqrt%28+%288%29%5E2-4%282%29%2815%29+%29%29%2F%282%282%29%29 Plug in a=2, b=8, and c=15


x+=+%28-8+%2B-+sqrt%28+64-4%282%29%2815%29+%29%29%2F%282%282%29%29 Square 8 to get 64.


x+=+%28-8+%2B-+sqrt%28+64-120+%29%29%2F%282%282%29%29 Multiply 4%282%29%2815%29 to get 120


x+=+%28-8+%2B-+sqrt%28+-56+%29%29%2F%282%282%29%29 Subtract 120 from 64 to get -56


x+=+%28-8+%2B-+sqrt%28+-56+%29%29%2F%284%29 Multiply 2 and 2 to get 4.


x+=+%28-8+%2B-+2i%2Asqrt%2814%29%29%2F%284%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%28-8%2B2i%2Asqrt%2814%29%29%2F%284%29 or x+=+%28-8-2i%2Asqrt%2814%29%29%2F%284%29 Break up the expression.


x+=+%28-4%2Bi%2Asqrt%2814%29%29%2F%282%29 or x+=+%28-4-i%2Asqrt%2814%29%29%2F%282%29 Reduce


So the answers are x+=+%28-4%2Bi%2Asqrt%2814%29%29%2F%282%29 or x+=+%28-4-i%2Asqrt%2814%29%29%2F%282%29 which are both complex (ie they are NOT real solutions)


which approximate to x=-2%2B1.871%2Ai or x=-2%2B1.871%2Ai

Answer by oscargut(2103) About Me  (Show Source):
You can put this solution on YOUR website!
P(x)=2x^2+8x+15=0
then
x+=+%28-8+%2B-+sqrt%28+8%5E2-4%2A2%2A15+%29%29%2F%282%2A2%29+=
x+=+%28-8+%2B-+sqrt%28+8%5E2-4%2A2%2A15+%29%29%2F%282%2A2%29+=
x+=+%28-8+%2B-+sqrt%28+-56+%29%29%2F%284%29+
then
P(x)=0 has not real solutions

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
2x%5E2+%2B+8x+%2B+15+=+0
Use the quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
where a+=+2
b+=+8
c+=+15
x+=+%28-8+%2B-+sqrt%28+8%5E2-4%2A2%2A15+%29%29%2F%282%2A2%29+
x+=+%28-8+%2B-+sqrt%28+64+-+120+%29%29%2F4+
x+=+%28-8+%2B-+sqrt%28+-56+%29%29%2F4+
x+=+%28-8+%2B-+2%2Asqrt%2814%29i%29%2F4+
x+=+-2+%2B+%28sqrt%2814%29i+%2F+2%29+ and
x+=+-2+-+%28sqrt%2814%29i+%2F+2%29+
I checked one of the answers, and it appeared to
check OK